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FUNDAMENTAL  SOURCES 
OF  EFFICIENCY 


BY 

FLETCHER  DURELL,  Ph.D. 

HEAD  OF  THE  MATHEMATICAL  DEPARTMENT  OF  THE  LAWRENCEVILLE  SCHOOL  ; 
AUTHOR  OF  A  SERIES  OF  MATHEMATICAL  TEXTBOOKS 


PHILADELPHIA  AND  LONDON 

J.   B.   LIPPINCOTT  COMPANY 

1914 


PREFACE 

The  present  work  is  an  attempt  to  analyze  the  various  forms  and 
sources  of  efficiency  into  a  few  elemental  principles.  It  is  felt  that 
the  study  of  such  primal  elements  will  not  only  aid  in  the  mastery  of 
efficiency  in  a  given  field,  but  will  prevent  this  important  idea  from 
assuming  a  narrow  meaning  and  thus  leading  to  limited  or  even,  in 
some  respects,  harmful  results. 

The  above  treatment  of  the  subject  also  facilitates,  on  the  one  | 
hand,  the  use  of  efficiency  principles  in  all  the  various  details  of 
work  and  experience  and,  on  the  other,  their  application  in  the; 
formation  of  a  general  philosophy  of  life. 

While  the  book  has  been  cast  in  a  form  adapted  to  general  read- 
ing, groups  of  exercises  have  been  inserted  which,  it  is  hoped, 
will  add  to  its  value  if  it  is  used  as  a  textbook  in  any  institution 
where  the  principles  of  efficiency  are  taught  either  generally  or  in 
any  specific  field. 

It  is  also  believed  that  such  a  presentation  of  the  principles  of 
efficiency  may  throw  light  on  the  problem  of  vocational  and  cultural 
studies,  and  perhaps  suggest  how  the  study  of  the  principles  of 
efficiency,  as  such,  may  be  made  a  central  study  in  educational 
systems,  helping  to  give  both  vocational  and  cultural  values  to 
other  more  conventional  studies. 

The  leading  ideas  contained  in  this  book  were  suggested  to  the 
author  when  reading  the  philosophy  of  Herbert  Spencer  more  than 
twenty  years  ago.  The  importance  of  investigating  the  elements 
which  constitute  fitness,  that  is,  efficiency,  becomes  evident  as  soon 
as  the  principle  of  the  survival  of  the  fittest  is  recognized.  While 
all  the  principal  ideas  in  the  book  were  thus  arrived  at  before  the 
present  energetic  movement  toward  efficiency  in  more  or  less  con- 
crete fields  arose,  new  light  and  many  important  details  have  been 
obtained  from  a  reading  of  the  publications  of  the  Efficiency  So- 
ciety, and  the  works  of  writers  like  F.  W.  Taylor,  Harrington 
Emerson,  and  Hugo  Miinsterburg. 

The  writer  wishes   to   express  his   indebtedness   to   Ida   Kruse 
McFarlane  and  Charles  William  Cuno  of  the  Department  of  Effi-  )  f 
ciency.  University  of  Denver,  who  have  kindly  read  the  manuscript 
and  made  important  suggestions  concerning  the  same. 


CONTENTS 


CHAPTER  PAGE 

I.    DEFINITIONS  AND  FIRST   PRINCIPLES i 

II.    REUSE     IS 

III.  THE  UNIT  AND  ITS  MULTIPLIER 34 

IV.  THE  GROUP   56 

V.     MULTIPLICATIVE    GROUPS    70 

VL  ORDERS   OF   MATERIAL 95 

VII.  EXTERNALITY     itt 

VIII.  UNIFORMITY  AND   DIVERSITY    130 

IX.  EXPENDITURES  AND  RESULTS   152 

X.  SYMBOLISM    164 

XL  DIRECTIVE    192 

XII.  KINEMATIC  AND  DYNAMIC  210 

XIII.  RHYTHM    230 

XIV.  DIALECTIC    249 

XV.  LIMITATION    265 

XVI.    ERROR  AND  PARADOX   281 

XVII.    COMBINATIONS  OF  EFFICIENTS.    SUMMARY 301 

XVIII.    APPLICATIONS    309 

APPENDIX  A.    The  Categories  and  a  Philosophy  of  Life 333 

B.     Historical  Survey  350 


CHAPTER  I 

PRELIMINARY  SURVEY.     DEFINITIONS 

Recent  Advances  in  Efficiency 

In  the  year  1900  a  competent  authority  estimated  that  the  cost 
of  unskilled  labor,  such  as  digging  dirt  and  carrying  burdens,  whem. 
done  by  man  unaided,  was  one  thousand  times  as  great  as  the  cost 
of  the  same  labor  when  done  by  the  aid  of  the  best  steam  engines. 
But  even  since  that  statement  was  made,  there  has  been  remarkable 
progress.  For  instance  the  Diesel  oil  and  tar  engine,  which  is. 
three,  or  under  some  circumstances  four  times  as  efficient  as  the 
steam  engine,  has  been  invented  and  come  into  use. 

When  he  was  a  young  man  Harrington  Emerson,  on  one  oc- 
casion, had  an  opportunity  to  watch  the  work  of  digging  the  Suez 
Canal.  He  thus  describes  the  crude  way  in  which  part  of  the  dig- 
ging was  being  done :  ''Many  of  the  workers  were  girls  digging  up 
the  sand  with  their  hands,  throwing  it  into  the  rush  basket  each  had 
woven  for  herself,  lifting  the  baskets  to  their  heads,  and  carrying 
the  load  of  20  or  30  pounds  a  hundred  feet  up  the  bank  and  dump- 
ing it."  He  calls  attention  to  the  contrast  of  this  method  of  exca- 
vating and  removing  earth  with  that  used  in  digging  the  Panama 
Canal.  At  the  latter  place  the  digging  has  been  done  almost  en- 
tirely by  steam  scoops,  each  Hfting  two  or  more  cubic  yards  of 
dirt  at  a  single  stroke.  The  earth  has,  in  some  cases,  been  removed 
for  twenty  miles  by  trains  of  cars,  and  the  tracks  on  which  these 
cars  ran,  when  a  change  in  their  position  became  necessary,  were 
moved  in  large  sections  at  a  single  operation.  Yet  in  the  highly 
efficient  process  of  digging  the  Panama  Canal,  many  improvements 
were  made  from  time  to  time.  It  was  estimated  that  in  this  work 
in  the  year  1912  a  ton  of  dynamite  was  twice  as  effective  as  in  the 
year  1908. 

Nor  has  the  advance  in  the  efficiency  of  skilled  labor  been  less 
noteworthy  than  that  in  such  crude  and  fundamental  work  as  dig- 
ging dirt.  For  instance  in  the  weaving  of  cotton  fabrics,  the  use 
of  power  machinery  has  increased  the  efficiency  of  a  workman  at 
least  eightfold. 


2  SOURCES  OF  EFFICIENCY 

Primitive  methods  of  agriculture,  as  compared  with  hunting  and 
fishing,  increase  the  productivity  of  the  land  200  times.  Here 
again,  the  use  of  machinery  and  other  improved  methods  have 
greatly  increased  the  efficiency  of  man's  labor.  Thus  ''between  the 
years  1830  and  1896  the  time  of  human  labor  required  for  the 
production  of  a  bushel  of  wheat  was  reduced  from  three  hours  to 
ten  minutes,  and  the  cost  of  the  human  labor  to  produce  this  bushel 
declined  from  17%  cents  to  3}^  cents". 

In  the  year  1866  the  death  rate  of  New  York  City  was  34  per 
thousand;  in  the  year  1912  this  rate  had  been  reduced  to  14. i  per 
thousand.  This  means  that  twelve  years  have  been  added  to  the 
length  of  the  average  human  life  in  that  city.  Similar  illustrations 
might  be  given  of  increased  efficiency  in  the  various  other  depart- 
ments of  human  activity. 

Opportunities  for  Further  Increases  in  Efficiency 

In  spite  of  the  large  advances  which  have  been  made,  even  a 
slight  examination  shows  that  opportunities  exist  for  large  exten- 
sions of  the  efficiencies  which  have  been  mentioned.  Even  in  the 
Diesel  engine  nearly  two  thirds  of  the  fuel  energy  is  wasted.  Ow- 
ing to  losses  in  mining  coal,  and  in  converting  coal  energy  into 
electric  light,  only  a  little  over  one  half  of  i  per  cent  of  the 
energy  latent  in  coal  as  it  lies  in  the  ground  is  utilized  by  man  in 
using  coal  as  a  source  of  light. 

In  the  fundamental  industry  of  agriculture,  an  efficiency  expert 
like  Harrington  Emerson  estimates  the  farms  in  the  United  States 
as  about  30  per  cent  efficient.  At  the  Conservation  Congress  in 
the  year  191 1,  the  statement  was  made  that  one-third  of  the  barn- 
yard manure  in  the  United  States  is  wasted,  and  that  this  means 
an  annual  loss  of  $800,000,000.  In  the  World's  Work  in  the  year 
1906,  it  was  stated  that  "all  authorities  are  now  agreed  that  we 
might  double  the  yield  of  our  principal  crops".  In  his  address  to 
the  Pennsylvania  Pilgrims,  May  1913,  President  Van  Hise  of  the 
University  of  Wisconsin  said :  "We  know  enough  about  agriculture 
so  that  the  agricultural  production  of  the  country  could  be  doubled 
if  the  knowledge  were  applied.  We  know  enough  about  disease  so 
that  if  the  knowledge  were  utilized  infectious  and  contagious  disease 
would  be  substantially  destroyed  in  the  United  States — and  that 
within  a  score  of  years.  We  know  enough  about  eugenics  so  that 
if  the  knowledge  were  applied  the  defective  classes  would  disap- 


PRELIMINARY    SURVEY  3 

pear  within  a  generation.     Similarly  in  other  fields  our  knowledge 
has  expanded  far  beyond  utilization." 

Growing  Need  of  Increased  Efficiency 

Not  only  do  opportunities  for  increased  efficiency  thus  exist,  but 
there  is  also  an  increasing  need  for  the  development  and  applica- 
tion of  such  methods.  On  February  14,  1912,  President  Taft  signed 
the  bill  for  the  admission  of  Arizona  as  the  forty-eighth  and  last 
state  in  the  Union.  Henceforth  the  people  of  the  United  States 
must  look  forward  primarily,  not  to  new  territory,  but  to  the  best 
possible  use  of  the  resources  now  in  their  possession.  The  same 
principles  apply  essentially  to  the  world  as  a  whole.  The  leading 
nations  have  explored  and  taken  possession  of  all  the  productive 
parts  of  the  earth's  surface.  By  the  use  of  steel  and  electricity 
this  process  has  recently  been  brought  to  a  conclusion  with  great 
suddenness.  Henceforth  the  law  of  the  survival  of  the  fittest  will 
have  a  new  and  more  crushing  power. 

Increasing  Value  of  Efficiency 

On  the  other  hand  improved  methods  of  efficiency  will  now  have 
an  ever  increasing  value  for  those  who  know  how  to  master  and 
apply  them.  Of  the  110,000  species  of  flowering  plants  known  to 
exist  in  the  world,  less  than  i  per  cent  have  been  studied  in  any 
adequate  way  and  reduced  to  man's  service.  The  non-flowering 
plants  and  the  animal  life  of  the  world  has  been  studied  and  uti- 
lized in  an  even  smaller  degree.  Quite  as  great  is  the  wealth 
which  man  can  make  by  his  own  exertions.  Thus  in  the  field  of 
chemistry,  between  the  years  1883  and  1900  the  number  of  carbon 
compounds  increased  from  16,000  to  67,000.  As  yet  but  few  of 
these  products  have  been  fully  studied  and  employed.  Humus,  be- 
cause it  improves  the  texture  of  the  soil,  conserves  moisture,  sup- 
plies food  to  the  growing  plant,  and  is  the  home  of  the  nitrogen 
fixating  bacteria,  is  one  of  the  most  important  elements  in  agri- 
culture. Yet  notwithstanding  the  vast  and  manifold  investigations 
of  science,  the  Encyclopedia  Brittanica  says  concerning  humus, 
"little  is  known  with  regard  to  its  chemical  constitution".  Hence 
man's  knowledge  of  the  most  efficient  way  to  use  humus  is  cor- 
respondingly limited,  and  an  important  field  here  lies  open  by  which 
to  obtain  new  power. 

Improved  methods  of  travel  and  communication  l)ring  each  of  the 


4  SOURCES  OF  EFFICIENCY 

world's  inhabitants  into  ever  closer  touch  with  its  artistic  treas- 
ures, its  literature,  scenery,  and  history.  Without  proper  methods 
for  its  mastery,  the  vast  mass  of  culture  wealth  thus  made  access- 
ible, may  become  a  burden  or  even  a  danger.  With  adequately 
developed  methods  of  assimilation,  it  becomes  a  near  and  instant 
wealth  to  every  person. 

Hence  supreme  need  and  supreme  opportunity  alike  spur  on 
mankind  to  a  study  of  the  science,  art,  and  philosophy  of  achieving 
results.  It  is  desirable  to  analyze  the  concept  of  efficiency  until 
primal  units  of  it  are  obtained  which  can  be  used  in  many  ways 
each  day  by  the  individual  person,  can  be  taught  in  the  schools, 
and  developed  into  elaborate  systems. 

DEFINITIONS    AND    FIRST    PRINCIPLES 

Definition  of  Efficiency 

An  efficient  process  is  one  in  which  the  available  results  exceed 
the  expenditure.  Thus  if  a  farmer  expends  $1000  in  raising  a 
crop  and  receives  $1500  for  the  crop,  his  work  may  be  said  to  be 
efficient. 

Efficiency  is  the  property  of  being  efficient:  that  is,  of  producing 
results  in  excess  of  expenditures. 

The  degree  of  efficiency  of  a  process  is  the  ratio  of  the  available 
result  of  the  process  to  the  expenditure.  Thus  in  the  above  illu- 
stration the  degree  of  efficiency  is  $1500  -^  $1000,  or  3/2.  Often 
"degree  of  efficiency"  is  shortened  to  "efficiency",  as  when  we  say 
that  the  efficiency  of  a  process  is  2,  or  twofold. 

In  case  the  degree  of  efficiency  is  less  than  one  or  unity,  the  given 
process  is  one  of  loss  or  waste.  Thus  if  a  farmer  spends  $1000  in 
raising  a  crop  of  wheat  and  receives  only  $800  for  the  crop,  the 
efficiency  of  the  process  is  the  fraction  4/5,  serving  to  indicate  the 
degree  of  loss  involved. 

Principal  Kinds  of  Efficiency 

Relative  efficiency  is  the  degree  of  efficiency  in  a  process  in  com- 
parison with  the  efficiency  in  a  like  process  taken  as  standard.  Thus 
if  land  which  should  produce  32  bushels  of  wheat  per  acre  is  being 
made  to  yield  only  24  bushels  per  acre,  the  efficiency  of  the  process 
of  agriculture  involved  is  75  per  cent.  Or  if  one  farmer  raises  20 
bushels  of  wheat  per  acre  while  another  farmer  raises  24  bushels 


DEFINITIONS  5 

per  acre  on  the  same  kind  of  land  the  efficiency  of  the  second  farmer 
as  compared  with  the  first  is  24  -^  20,  or  6/5. 

In  comparison  with  relative  efficiency  the  first  definition  of  effi- 
ciency given  is  a  definition  of  absolute  or  independent  efficiency. 

A  case  of  homogeneous  efficiency  is  one  in  which  the  material 
expended  and  the  results  obtained  are  of  the  same  kind.  Illustra- 
tions are  the  expenditure  of  money  to  obtain  more  money;  or  the 
planting  of  grain  to  procure  more  grain  of  the  same  kind;  or  the 
sacrifice  of  present  happiness  to  obtain  more  happiness  in  the 
future. 

A  case  of  heterogeneous  efficiency  is  one  in  which  the  output 
obtained  is  different  in  kind  from  the  material  expended.  Particu- 
lar instances  are  the  burning  of  coal  to  produce  light,  or  the  taking 
of  strychnine  in  small  doses  to  improve  one's  health. 

It  is  important  to  note  that  the  degree  of  a  case  of  heterogeneous  efficiency 
cannot  be  expressed  or  measured  directly.  For  the  quantities  com- 
pared in  any  ratio  must  be  of  the  same  kind.  Thus  bushels  cannot  be 
divided  by  dollars,  nor  light  by  coal,  nor  health  by  arsenic.  Two  ways, 
however,  exist  by  one  or  both  of  which  the  degree  of  a  case  of  heterogeneous 
efficiency  may  usually  be  expressed.  The  first  of  these  methods  consists  in 
transforming  the  given  case  into  one  of  homogeneous  efficiency  and  then 
treating  the  result  directly.  Thus  if  money  is  expended  to  produce  wheat 
which  is  consumed  on  the  farm  and  thereby  results  in  health  and  happiness 
the  process  is  heterogeneous ;  but  if  the  wheat  crop,  instead  of  being  consumed 
on  the  farm,  is  converted  into  money,  the  process  becomes  homogeneous 
and  its  efficiency  can  be  expressed  as  the  ratio  of  the  sum  of  money  received 
to  that  expended.  Similarly  if  the  money  received  from  the  sale  of  light 
be  compared  with  that  expended  in  producing  the  light,  the  efficiency  involved 
is  determined  numerically. 

The  second  method  of  measuring  heterogeneous  efficiency  is  that  of 
expressing  the  efficiency  in  the  relative  form;  that  is,  comparing  the  output 
in  a  given  case  with  that  in  another  case  where  the  expenditure  is  the  same, 
the  latter  case  being  taken  as  a  standard.  Thus  if  the  burning  of  a  ton  of 
coal  will  produce  a  given  number  of  units  of  light  in  one  case,  but  will 
produce  twice  as  many  units  in  another  case,  in  the  latter  case  the  fuel 
efficiency  is  twice  what  it  is  in  the  former.  Or,  to  look  at  the  matter  from 
a  somewhat  different  point  of  view,  if  a  given  current  of  electricity  on 
passing  through  tungsten  filaments  will  produce  2^  times  as  much  light  as 
when  passing  through  carbon  filaments,  the  efficiency  of  the  tungsten  filament 
is  said  to  be  2>^  times  that  of  the  carbon.  Similarly  if  a  given  area  of  land 
will  support  two  persons  who  live  by  hunting  and  fishing,  but  when  used 
agriculturally  will  support  300  persons,  the  efficiency  of  the  agricultural  use 
of  the  land  as  compared  with  its  use  for  hunting  is  150. 


6  SOURCES  OF  EFFICIENCY 

Qualitative  Efficiency 

In  some  cases  the  results  of  a  process  are  so  abstract  or  complex 
that  it  is  not  possible  to  reduce  them  to  a  numerical  basis.  Instances 
are  the  expenditure  of  money  to  procure  health  or  to  save  Hfe.  This 
abstractness  or  complexity  may  characterize  either  the  expenditure 
or  the  results  or  both  of  these.  As  illustrations  we  have  the  sacri- 
fice of  home  associations  in  order  to  make  money  in  a  foreign  land, 
or  of  health  in  order  to  obtain  an  education  and  power  of  social 
service.  Hence  we  may  say  in  general  that  qualitative  (or  mass) 
'efficiency  is  efficiency  whose  existence  is  evident  but  which  cannot 
be  expressed  in  an  exact  numerical  form  on  account  of  the  abstract- 
ness or  complexity  of  some  of  the  elements  involved. 

Efficiency  Relative  to  an  Ideal 

Certain  important  cases  of  relative  efficiency  call  for  special 
mention. 

The  first  is  efficiency  relative  to  an  ideal  or  perfect  standard. 
Thus  a  perfect  steam  engine  would  be  one  which  converts  all  the 
energy  latent  in  the  coal  consumed  by  it,  into  mechanical  power. 
No  steam  engine,  however,  can  convert  more  than  i8  per  cent  of  its 
fuel  into  power.  Hence  the  fuel  efficiency  of  a  steam  engine  cannot 
exceed  i8  per  cent.  That  of  a  small  steam  engine  is  frequently  as 
low  as  I  per  cent.  There  are  indications  that  the  amount  of  sugar 
in  a  sugar  beet  cannot  be  made  to  exceed  about  17.5  per  cent.  A 
further  increase  seems  to  cause  the  vegetative  processes  of  the  beet 
to  degenerate  and  the  whole  organism  to  decay.  If  this  view  of 
the  matter  is  correct,  with  respect  to  the  ideal  beet  the  degree  of 
efficiency  in  a  beet  containing  10.5  per  cent  of  sugar  is  10.5  -^  17.5, 
or  60  per  cent.  Similarly  if  a  pupil  solves  8  problems  out  of  10  on 
an  examination  paper,  his  efficiency  is  .80  with  respect  to  the  ideal 
which  consists  of  solving  all  of  the  problems. 

Bogey  and  Competitive  Efficiency 

The  second  form  of  relative  efficiency  is  that  with  respect  to 
some  degree  of  efficiency  taken  as  normal,  or  *'bogey",  under  given 
conditions.  Thus  if  the  thoroughly  trained  and  equipped  but 
average  workman  is  able  to  lay  2800  bricks  per  day,  a  workman 
who  lays  2240  bricks  has  an  efficiency  of  80  per  cent;  while  one 
who  lays  3220  bricks  has  an  efficiency  of  115  per  cent.  This  kind  of 
efficiency  may  be  termed  bogey  efficiency. 


DEFINITIONS  7 

In  the  third  place  we  have  what  may  be  termed  competitive 
efficiency.  By  this  is  meant  the  degree  of  one's  efficiency  in  com- 
parison with  that  of  one's  immediate  competitors.  Thus  if  with  a 
given  outlay  of  time  and  money  one  farmer  produces  only  1000 
quarts  of  milk  while  his  neighbors,  with  the  same  outlay,  produce 
1500,  the  competitive  efficiency  of  the  first  farmer  is  66%  per  cent. 
It  is  to  be  noted  that  the  competitors  involved  in  a  given  case  may 
fall  below,  equal,  or  exceed  bogey  efficiency.  The  importance  of 
the  matter  lies  in  the  fact  that,  when  a  man's  competitive  efficiency 
is  small,  he  may  be  undersold,  driven  from  business,  or  ruined  com- 
mercially. Efficiency  of  this  kind  which  does  not  reach  a  certain 
standard,  is  therefore  often  called  inefficiency  or  absolute  failure. 
Competitive  efficiency  is  recognized  in  such  statements  as  "He  has 
made  good",  or  'This  is  worth  while". 

Economy 

Cases  of  efficiency  may  be  relative  in  other  ways  as  with  respect 
to  the  emphasis  laid  on  expenditure  or  on  output.  For  instance,  in 
a  given  case,  it  may  be  desirable  to  strive  for  that  form  of  effi- 
ciency which  consists  of  diminishing  the  cost  instead  of  that  which 
is  characterized  by  an  increase  in  the  output.  This  form  of  effi- 
ciency is  usually  termed  economy.     Or,  in  general, 

Economy  is  a  form  of  efficiency  in  which  the  output  compared 
with  that  in  a  standard  case  is  unchanged  but  the  expenditure  is 
diminished.  Thus  if  a  farmer  who  has  been  raising  1000  bushels 
of  wheat  at  a  cost  of  $470  is  enabled  in  a  later  year  to  produce  this 
same  amount  of  wheat  at  a  cost  of  $360,  the  process  is  primarily 
one  of  economy.  Hence,  in  general,  efficiency  means  primarily  an 
increase  in  results;  economy,  a  diminution  in  expenses.  Economy 
is  thus  the  inverse  of  efficiency.  The  proverb  "A  dollar  saved  is  a 
dollar  made"  illustrates  the  fact  that  economy  and  efficiency  are  two 
aspects  of  the  same  thing. 

It  is  frequently  convenient  to  treat  cases  of  relative  efficiency  as  cases  of 
relative  economy ;  that  is,  to  estimate  degrees  of  efficiency  by  a  comparison 
of  costs  instead  of  outputs.  This  is  illustrated  by  comparing  the  cost  of 
raising  a  bushel  of  wheat  on  one  farm  with  that  on  another.  For  example 
if  one  farmer  raises  a  bushel  of  wheat  at  a  cost  of  48  cents  and  his  neighbor 
at  a  cost  of  40  cents,  the  efficiency  of  the  first  as  compared  with  the  second  is 
lf»  or  f,  or  83 >^  per  cent.  It  is  to  be  carefully  noted  that  in  forming 
this  ratio,  the  two  costs  are  compared  in  the  inverse  order  from  that  used  in 
determining  the  degree  of  efficiency  by  a  comparison  of  two  outputs. 


8  SOURCES  OF  EFFICIENCY 

Infinite  Efficiency 

Important  cases  of  efficiency  are  those  in  which  the  degree  of 
efficiency  is  immeasurably  large  (or  infinite).  As  examples  we 
have  all  those  cases  where  what  is  valueless  when  treated  in  one  way 
becomes  useful  when  treated  in  some  other  way.  For  instance 
some  forms  of  lignite  when  burned  directly  are  valueless  for  power 
generating  purposes,  but  become  valuable  when  converted  into  gas 
and  used  in  a  gas  engine.  Other  and  still  more  important  cases  are 
those  of  the  conversion  of  loss,  waste,  or  defeat  into  results  having 
a  positive  value.  An  instance  is  that  of  saving  life  in  a  case  where 
death  has  hitherto  resulted  uniformly,  as  in  certain  kinds  of  surgical 
operations.  Another  instance  of  infinite  efficiency  is  that  of  using 
two  points  to  represent  a  straight  line,  or  of  the  drawings  called  a 
plan  and  elevation  to  represent  a  building. 

Terms  related  to  Efficiency 

Usefulness  means  efficiency  regarded  as  a  broad  qualitative  fact 
and  with  but  slight  emphasis  on  the  quantitative  elements  involved. 

Utility  is  the  same  as  usefulness  except  that  in  utility  results  are 
usually  more  concrete,  or  more  definitely  realized. 

Efficacy  (or  effectiveness)  is  a  form  of  efficiency  in  which  em- 
phasis is  laid  on  the  complete  attainment  of  a  specified  end,  com- 
paratively small  attention  being  paid  to  the  cost  involved. 

It  is  convenient  at  times  to  denote  cases  of  waste  or  loss  by  the 
term  negative  efficiency. 

Knowledge  of  Equivalence  an  Aid  to  Efficiency 

Before  concluding  the  discussion  of  cases  of  relative  efficiency,  a 
word  should  be  said  as  to  the  relation  of  efficiency  processes  to  the 
equivalence  or  invariant  processes  with  which  they  are  associated. 
In  certain  respects  the  results  of  a  process  must  be  equivalent  to 
the  data  involved.  Thus  by  the  laws  of  the  conservation  of  energy 
and  of  matter,  the  amount  of  force  and  of  matter  in  the  entire 
results  of  a  process  cannot  diflfer  from  those  in  the  data.  Never- 
theless in  a  given  case  the  amount  of  those  results,  which  are  usable 
or  available  for  a  given  purpose,  may  differ  from  the  amount  availa- 
ble in  the  data.  Thus  when  a  given  amount  of  food  is  fed  to  one 
kind  of  cow,  more  milk  is  often  obtained  than  when  the  same  amount 
of  food  is  fed  to  another  variety  of  cow.  In  the  present  investiga- 
tion we  take  this  principle  of  profitable  non-equivalence  between 


DEFINITIONS  9 

datum  and  result  in  certain  processes  as  a  fact  or  axiom  and  try 
to  take  the  utmost  advantage  of  it.  In  the  course  of  our  investiga- 
tion we  shall  find  that  equivalence  laws  and  facts  are  useful  in  ob- 
taining efficiency  results.  An  illustration  is  the  fact  that  when  coal 
is  burned  under  the  boiler  of  a  steam  engine  only  15  per  cent  of  the 
power  latent  in  the  coal  is  converted  into  mechanical  energy,  the  rest 
being  lost  as  friction  in  parts  of  the  engine,  or  as  heat  which  passes 
up  the  chimney,  or  radiates  from  the  parts  of  the  engine.  If,  how- 
ever, the  coal  is  first  converted  into  gas  and  then  used  in  a  gas 
engine,  the  amount  of  useful  energy  obtained  is  often  increased 
threefold.  A  knowledge  of  the  equivalences  concerned  has  been 
an  important  aid  in  obtaining  this  more  efficient  result. 

COMPLEX  CASES  OF   EFFICIENCY 

Efficiency  Factors  Acting  in  Succession 

An  efficiency  process  may  often  be  separated  into  a  number  of 
parts  acting  in  succession,  each  part  acting  upon  the  results  of  a 
preceding  part.  The  resultant  efficiency  of  all  the  parts  is  then 
obtained  by  taking  the  product  of  the  respective  efficiencies  of  the 
different  parts.  By  way  of  illustration  we  may  consider  a  metal 
cutting  machine  which  has  been  run  for  5  hours  per  day  at  a  speed 
of  10  revolutions  per  minute  and  which  does  its  cutting  by  means 
of  a  fine  diamond  point.  If  the  machine  is  afterwards  run  8 
hours  per  day  with  a  speed  of  45  revolutions  per  minute  and  a  round 
nose  tool  with  a  cutting  end  10  times  as  wide  as  the  diamond  point 
is  used  for  the  cutting,  the  efficiency  elements  of  time,  speed,  and 
width  of  cut  are  increased  8/5,  9/2,  and  tenfold  respectively.  Hence 
the  efficiency  of  the  new  process,  as  compared  with  that  of  the  old, 
is  f  X  f  X  10,  or  'J2.  When  elements  of  efficiency  are  combined 
in  this  way,  they  may  be  regarded  as  acting  tandem  and  the  resultant 
obtained  called  tandem  or  multiplicative  efficiency. 

Parallel  Efficiency  Factors 

In  other  cases  of  resultant  efficiency  the  elements  concerned  act 
parallel  to  each  other,  and  the  degree  of  efficiency  in  the  process  as 
a  whole  is  equal  to  the  average  degree  of  efficiency  of  the  compo- 
nents. Thus  if  a  farmer  is  raising  four  crops  at  the  same  time,  all  of 
equal  importance,  and  their  respective  efficiencies  are  .80,  .90,  .86, 
.92,  his  efficiency  for  the  year  is  the  average  of  these  rates,  or  .87. 
In  the  same  way  the  efficiency  of  a  student  is  sometimes  determined 


10  SOURCES  OF  EFFICIENCY 

by  his  average  grade  in  all  the  subjects  pursued  by  him.  If  however 
the  elements  involved  in  a  given  case  are  of  unequal  importance,  to 
obtain  the  resultant  efficiency  it  is  necessary  to  multiply  each  ele- 
mental efficiency  by  a  number  which  indicates  its  weight  or  impor- 
tance, to  take  the  sum  of  all  the  products  and  divide  the  sum  obtained 
by  the  sum  of  all  the  weights.  Thus  if  the  respective  efficiencies  of 
four  crops  raised  by  a  farmer  are  .60,  .90,  .80,  .72,  and  the  second  and 
third  crops  are  each  twice,  and  the  last  three  times  as  important  as 
the  first,  his  resultant  efficiency  is   -60+2 X. 90+^X^+3 X.72  ^^  ^^^ 

Tandem  and  Parallel  Efficiencies  Combined 

In  is  evident  that  mixed  cases  of  efficiency  also  occur,  in  the 
sense  that  some  of  the  elements  involved  act  in  tandem  or  multipli- 
cative fashion  in  whole  or  part,  and  others  are  parallel  or  additive 
in  relation.  For  instance  while  the  chief  crops  of  a  farmer  during  a 
given  year  may  be  developed  in  parallel  fashion,  the  operations  in- 
volved in  raising  one  or  more  of  the  crops  may  act  in  multiplicative 
succession.  Thus  the  manner  of  preparing  the  seed  bed  affects 
the  development  of  the  seed,  care  and  efficiency  in  selecting  the  seed 
influence  all  later  processes,  and  so  on.  Also  if  the  crops  are 
rotated  from  year  to  year  the  efficiency  of  any  one  crop  influences 
the  efficiency  of  the  crops  which  follow  in  succeeding  years.  This 
may  also  result  in  certain  multiplicative  cross  relations  during  any 
one  year.  Thus  large  hay  and  corn  crops  will  supply  feed  for 
many  cattle  which  in  turn  will  supply  a  larger  amount  of  fertilizer 
for  several  later  crops. 

Another  Method  of  Analyzing  Efficiency  Processes 

Emphasis  should  be  laid  in  this  connection  on  what  is  for  our 
purpose  a  still  more  important  method  of  analyzing  an  efficiency 
process  into  constituent  elements.  To  illustrate  this  method  we  take 
the  case  of  a  particular  crop  raised  by  a  farmer,  as  a  crop  of  wheat. 
The  agriculturist  obtains  efficiency  in  preparing  the  seed  bed  of  the 
crop  by  several  distinct  means  one  of  which,  for  instance,  is  the 
group  principle  in  the  form  of  the  gang  plow  and  also  of  the  extra 
wide  harrow.  The  group  as  a  source  of  efficiency  is  also  found  in 
the  drill  used  in  sowing  the  seed,  and  in  the  reaper  used  in  harvest- 
ing the  grain.  In  some  form,  often  in  several  forms,  it  is  an  aid 
in  the  efficient  marketing  of  the  crop.  Other  general  primal  effi- 
ciency principles  are  at  work  in  the  various  concrete  divisions  of 


DEFINITIONS  II 

the  process  which  have  been  enumerated.  Even  the  division  of  the 
process  into  such  parts  as  fertilizing  the  ground,  preparing  the  seed 
bed,  planting  the  seed,  etc.,  for  separate  study,  is  an  application  of 
one  of  these  primary  principles,  viz. :  that  of  the  use  of  units,  or  of 
diversity.  Owing  to  their  fundamental  and  inclusive  nature,  a  thor- 
ough grasp  of  these  primal  efficiency  agencies  will  mean  increased 
efficiency  in  the  various  departments  of  life.  These  primary  effi- 
ciency principles  will  be  taken  up  one  by  one  in  chapters  which  fol- 
low and  each  investigated  as  closely  as  possible.  Afterward  they 
will  be  considered  to  some  extent  in  combination. 


EXERCISE  1 

Determine  the  degree  of  efficiency  in  each  of  the  following  cases: 

1.  A  farmer  expended  $2000  in  raising  a  crop  of  corn  and  received  $2800 
for  the  crop. 

2.  A  farmer  spends  $1200  in  raising  a  crop  of  wheat  and  receives  but 
$1000  for  the  crop, 

3.  Land  which  should  yield  80  bushels  of  corn  per  acre  is  producing  but 
56  bushels  per  acre. 

4.  By  an  expenditure  of  $800,  2,200  bushels  of  potatoes  which  sold  for 
80  cents  a  bushel  were  produced. 

5.  A  machine  capable  of  400  revolutions  per  minute  is  making  250  revolu- 
tions per  minute. 

6.  It  has  been  estimated  that  ten  square  miles  of  land  used  for  hunting 
and  fishing  will  support  2  persons,  while  the  same  land  when  used  agricultur- 
ally will  support  1000  persons. 

7.  In  a  certain  town  the  light  given  by  a  16  candle  power  carbon  bulb 
costs  M  cents  per  hour,  while  that  given  by  a  32  candle  power  tungsten 
bulb  costs  Vz  cent  per  hour. 

8.  On  one  field  an  expenditure  of  $800  produced  a  yield  of  2000  bushels 
of  potatoes,  and  on  another  field  $1200  produced  4200  bushels. 

9.  A  field  which,  by  following  the  best  available  methods,  could  have  been 
planted  in  8  days,  was  actually  planted  in  10  days. 

10.  It  costs  $4000  per  annum  to  run  a  certain  poultry  establishment,  and 
the  annual  receipts  average  $4800. 

11.  A  man  who  should  work  8  hours  per  day,  on  account  of  ill  health  works 
on  the  average  2  hours  and  15  minutes  per  day. 

12.  A  gold  mine  which  cost  $400,000  at  first  paid  8  per  cent  dividends,  but 
later  when  operated  by  improved  methods  paid  dividends  of  20  per  cent. 

13.  Between  the  years  1840  and  1900  the  per  cent  of  sugar  in  the  sugar 
beet  was  increased  from  5%  to  13. 

14.  When  coke  is  burned  directly,  45  per  cent  of  its  energy  is  utilized.  If 
it  is  converted  into  water  gas  before  it  is  consumed,  82  per  cent  of  its 
energy  is   utilized. 


12  SOURCES  OF  EFFICIENCY 

15.  At  one  time  6i  hours  of  labor  by  one  man  were  necessary  to  cultivate 
one  acre  of  wheat.  At  the  present  time  this  number  of  hours  has  been 
reduced  to  3. 

16.  When  the  Americans  acquired  the  Philippine  Islands,  they  found  the 
natives  transporting  mahogany  logs  at  a  certadn  place  from  the  interior 
to  the  seashore  by  such  crude  methods  that  it  took  16  buffalos  and  20  men 
to  transport  one  log  a  distance  of  one  mile  per  day.  An  American  taught 
the  Filipinos  to  isaispend  one  end  of  a  log  from  the  axle  of  two  large  wheels, 
and  thus  made  it  possible  for  2  buffalos  and  2  men  to  transport  a  log 
20  miles  in  one  day.  If  a  day's  work  by  a  buffalo  is  taken  as  worth  50  cents, 
and  that  by  a  man  as  worth  the  same,  compute  the  efficiency  of  the  second 
process. 

17.  State  which  of  the  preceding  instances  are  cases  of  relative  efficiency. 
Also  which  are  cases  of  independent  or  absolute  efficiency. 

18.  State  which  are  cases  of  economy,  and  which  of  direct  efficiency. 

19.  State  which  are  cases  of  homogeneous  and  which  of  heterogeneous 
efficiency. 

Give  an  example  of  each  of  the  following  kinds  of  efficiency  and  determine 
the  degree  of  efficiency  in  each  illustration  given: 

20.  Economy  23.  Homogeneous  Efficiency 

21.  Direct  Efficiency  24.  Heterogeneous  Efficiency 

22.  Relative  Efficiency  25.  Bogey  Efficiency 

26.  Competitive   Efficiency 

27.  Give  an  example  of  the  transformation  of  a  case  of  heterogeneous  into 
homogeneous  efficiency. 

28.  At  one  time  40  hours  of  labor  produced  2  tons  of  hay.  Later  40  hours 
of  labor  produced  20  tons  of  hay.  Transform  these  statements  so  that 
they  shall  express  an  economy  instead  of  a  direct  efficiency. 

29.  At  one  time  100  hours  of  labor  produced  48  bushels  of  oats.  Later 
by  the  use  of  improved  methods  40  hours  of  labor  were  made  to  produce 
180  bushels  of  oats.  Transform  these  statements^  so  that  the  expenditure  of 
labor  in  the  two  cases  is  the  same.  Also  so  that  the  crop  obtained  is  the 
same. 

30.  Give  an  illustration  of  efficiency  and  transform  it  into  an  economy. 

31.  Give  an  illustration  of  economy  and  transform  it  into  an  efficiency. 

Find  the  resultant  degree  of  efficiency 

32.  In  a  process  in  which  the  efficiencies  of  the  four  constituent  (tandem) 
elements  are  3,  2,  5,  %  respectively. 

ZZ-  Are  .60,  .80,  .90,  .75  respectively. 

34.  Of  a  process  where  the  five  constituent  (parallel)  elements  are  ^,  5^, 
^2,  5-4.  5-2. 

35.  Where  the  three  (parallel)  elements  are  .60,  .84,  .72  respectively,  and 
the  second  and  third  elements  each  count  twice  as  much  as  the  first. 


DEFINITIONS 


13 


S6.  A  metal  cutting  machine  has  been  running  3V2  houns  per  day,  and 
making  18  revolutions  per  minute.  If  it  should  run  10  hours  per  day, 
make  80  revolutions  per  minute,  and  use  a  cutting  point  6  times  wider  than 
that  in  use,  how  many  fold  would  the  efficiency  of  the  machine  be  increased? 

37.  A  farmer  raises  four  crops  with  efficiencies  of  .60,  .80,  .70,  .50.  If  the 
second  and  third  crops  are  each  twice,  and  the  last  three  times  as  valuable 
as  the  first,  find  his  average  efficiency  for  the  year. 

38.  Give  a  numerical  illustration  of  resultant  efficiency  composed  of  tandem 
elements. 

39.  Also  of  one  of  parallel  elements. 

40.  Also  of  one  containing  both  tandem  and  parallel  elements. 

41.  Ascertain  the  methods  of  judging  milk  cattle,  horses,  and  a  corn  stalk 
with  ears,  and  determine  whether  each  of  these  is  a  case  of  tandem  or  of 
parallel  efficiency. 

42.  By  uising  an  auxiliary  instance  in  which  the  result  equals  the  cost, 
show  that  each  case  of  absolute  or  independent  efficiency  may  be  regarded 
as  a  case  of  relative  efficiency. 

43.  Ascertain  the  original  meaning  of  the  word  economy.  Is  this  word 
ever  used  in  its  original  or  some  similar  sense? 

44.  Give  an  example  of  infinite  negative  efficiency. 

45.  Give  an  illustration  of  a  process  which  is  efficient  when  judged  by  one 
standard  but  is  wasite  or  loss  when  judged  by  another. 

46.  Give  an  illustration  of  reciprocal  efficiency. 

47.  On  a  certain  field  80  days  labor  by  one  man  will  produce  a  yield  of 
300  bushels  of  corn,  while  90  days  labor  will  produce  a  yield  of  400  bushels. 
Which  method  of  cultivation  is  the  more  efficient  and  how  much? 

48.  Which  is  the  more  fundamental  test  of  efficiency  in  raising  a  given 
crop  in  a  given  country,  the  yield  per  acre,  or  that  per  workman?  Give 
reasons  for  your  answer. 

49.  Explain  the  meaning  of  the  proverb  "Strength  saved  is  strength  made." 
Also  of  "Economy  is  wealth." 

State  the  kind  or  kinds  of  efficiency  involved  in  each  of  the  following 
instances;  also  compute  the  degree  of  efficiency  wherever  possible: 

50.  The  office  expenses  of  a  given  business  were  $2750  annually.  After  the 
introduction  of  the  card  and  loose  leaf  ledger  system  of  keeping  accounts, 
the  annual  office  expenses  were  reduced  to  $1600. 

51.  In  Watt's  steam  engine  1/25  of  the  energy  in  coal  was  utilized.  In 
some  modern  steam  engines  1/6  of  this  energy  is  utilized. 

52.  The  employment  in  a  productive  way  of  capital  which  has  been  lying  idle. 
53-  The  efficiency  of  a  given  process  should  be  3/2  but  is  actually  only  5/4. 

54.  By  changing  the  seed  used  a  farmer  increased  the  yield  of  wheat  per 
acre  on  a  given  farm  from  20  bushels  to  24  bushels. 

55.  A  series  of  separate  pictures  on  a  moving  picture  film  when  thrown 
on  the  screen  in  succession  gives  the  impression  of  a  continuous  whole. 

56.  By  an  expenditure  of  $20,000,  gold  worth  $800  was  obtained  from 
sea  water. 


14  SOURCES  OF  EFFICIENCY 

57.  A  given  amount  of  grain  and  fodder  when  fed  to  beef  cattle  will 
produce  4000  lbs.  of  beef,  but  when  fed  to  milch  cows  will  produce  milk 
which  is  equivalent  in  food  value  to  18,000  lbs.  of  beef. 

58.  Reciprocating  steam  engines  on  the  average  consume  472  lbs.  of 
coal  per  horse  power  per  hour;  turbine  engines,  i^)41bs. ;  gas  engines,  i^  lbs. 

59.  In  a  certain  city  the  expenditure  of  $1,500,000  for  a  water  filtration  plant 
reduced  the  annual  death  rate  from  22  per  thousand  to  18  per  thousand. 

60.  In  'fattening  a  beef  steer  it  was  found  that  the  first  100  pounds  of 
increased  weight  in  the  animal  were  produced  by  730  pounds  of  grain  used  as 
food,  and  the  last  100  pounds  of  weight  required  1000  pounds  of  grain  food. 

61.  The  eificiency  of  a  given  business  firm  in  buying  is  .80,  in  manufacturing 
is  .95,  and  in  selling  is  .90. 

62.  The  use  of  an  improved  textbook  in  a  given  school  caused  30  per  cent 
more  of  the  pupils  to  pass  in  the  subject  taught  and  saved  the  teacher  much 
time  and  effort. 

63.  On  a  certain  railroad  when  operated  by  steam  90  lbs.  of  coal  on  the 
average  were  burned  to  send  a  train  of  cars  a  distance  of  one  mile.  After 
the  railroad  was  electrified  50  lbs.  of  coal  did  this  work. 

64.  In  a  certain  year  9,000,000  agricultural  workers  in  the  United  States 
produced  600,000,000  'bushels  of  wheat,  while  in  Europe  6o,ooc,ooo  farm 
laborers  produced  1,200,000,000  bushels  of  wheat. 

65.  In  a  certain  neighborhood  one  farmer  by  spending  $2,000  produces  crops 
worth  $4,000.  Another  farmer  by  spending  $2,000  produces  $3,000.  Com- 
pute the  absolute  efficiency  for  each  farmer.  Also  compute  the  relative 
efficiency  of  the  second  farmer  as  compared  with  the  first. 


CHAPTER  II 

REUSE 

Illustrations  of  Reuse 

A  cook  who  has  succeeded  in  inventing  a  new  recipe  frequently 
saves  herself  much  labor  by  preserving  this  recipe  and  using  it 
repeatedly.  Often  also  the  cook  does  mankind  a  service  by  giving 
the  recipe  to  other  cooks  to  use.  Similarly  a  man  who  has  made  a 
successful  speech  may  at  times  save  himself  much  work  by  writing 
out  the  speech  and  using  it  in  whole  or  in  part  on  other  occasions. 

The  automobile  is  possible  because  the  gas  engine,  the  pneumatic 
tire,  and  ball  bearings,  all  invented  in  some  other  connection,  have 
l)een  reused  in  combined  form  to  produce  the  motor  carriage.  The 
commission  form  of  city  government  originated  in  Galveston  after 
the  city  had  been  devastated  by  a  severe  storm,  and  has  since  been 
adopted  by  hundreds  of  other  cities. 

If  we  go  back  far  enough  in  human  history  we  find  a  primitive 
manlike  creature  who  had  been  in  the  habit  of  picking  up  from 
time  to  time  any  club  that  chanced  in  his  way,  and  of  using  it  as  an 
aid  in  killing  wild  animals  for  food.  To  this  progenitor  of  man  it 
occurred  at  some  time  to  keep  a  good  club  which  he  had  found  that 
he  might  use  it  again  and  thus  save  himself  the  labor  of  searching 
for  other  clubs.  This  act  of  his  lifted  his  life  to  a  new  level  of 
efficiency  and  indeed  constituted  a  distinct  epoch  in  human  progress. 

For  in  this  act  and  in  the  other  instances  given  above  we  have 
illustrations  of  a  primary  and  fundamental  principle  of  efficiency 
which  we  may  term  reuse  or  repeated  use.  This  is  the  first  of  the 
specific  efficiency  principles  which  we  shall  study. 

CLASSIFICATION 

Cases  of  repeated  use  may  be  classified  according  to  the  character 
of  the  objects  which  are  used  over  and  over  again. 

Classification  according  to  Materials  Reused 

Material  inorganic  objects  may  be  reused.  Instances  are  the 
repeated  use  of  a  spade,  a  gun,  or  a  silver  coin;  of  ammonia  when 

15 


l6  SOURCES  OF  EFFICIENCY 

used  over  and  over  again  in  an  ice-making  machine ;  or  of  sea  water^ 
which  by  being  reoxygenated  is  used  repeatedly  in  a  vivarium,  the 
expense  of  obtaining  a  new  supply  of  sea  water  each  day  being  there- 
by avoided.  The  basis  of  civilization  is  the  soil  which  has  been 
cleared  so  that  it  can  be  reused  in  raising  crops  in  successive  years 
and  which,  in  advanced  methods  of  cultivation,  will  even  produce  six 
or  seven  crops  in  one  season.  Similarly  all  the  material  objects 
which  enter  into  the  formation  of  tools  and  machinery,  including 
large  objects  like  buildings,  are  reused.  A  noticeable  case  is  the 
reuse  of  a  mold  or  pattern  in  manufacturing  metallic  objects. 

Living  organic  objects  are  frequently  reused  in  whole  or  part. 
The  amoeba  improvises  an  arm  or  mouth  out  of  its  substance  when 
opportunity  or  need  arises  for  the  use  of  such  a  member.  But 
higher  animals  have  organs  and  members  which  are  grown  once  for 
all  and  then  reused.  This  repeated  use  often  includes  not  merely 
reuse  for  one  given  purpose  but  in  many  different  ways.  Thus  the 
human  hand  is  used  repeatedly  not  merely  for  the  purpose  of 
grasping  a  specified  object  many  times  in  succession,  but  as  an 
instrument  by  which  to  strike,  push,  pull,  write,  swim,  gesture,  give, 
and  to  perform  a  variety  of  other  acts. 

The  advantage  in  using  domesticated  animals  instead  of  living 
by  the  chase  is  largely  the  gain  which  comes  from  reuse.  Thus  if 
a  wild  animal  is  killed  and  eaten  it  is  used  but  once.  Whereas  if  it 
is  kept  and  milked,  or  used  as  a  beast  of  burden,  or  in  breeding 
other  animals,  it  is  used  many  times  in  succession.  A  similar  ad- 
vantage led  to  the  change  from  torturing  and  killing  men  captured 
in  war,  to  keeping  them  as  slaves. 

In  fact  a  high  degree  of  social  organization  means  that  the  mem- 
bers of  society  are  using  and  reusing  each  other  in  many  ways  daily. 

Reuse  of  more  Abstract  Data 

Mental  data  are  also  capable  of  reuse.  Thus  by  the  aid  of 
memory  and  imagination,  we  reuse  perceptions,  feelings,  and  con- 
cepts. We  are  thereby  saved  the  labor  of  acquiring  these  data  anew^ 
and,  what  is  often  of  even  greater  importance,  acquire  a  surplus 
mental  energy  which  we  can  use  for  higher  purposes.  An  adequate 
analysis  would  also  show  that  we  reuse  mental  data  by  means  of  the 
reasoning  faculty  and  by  unconscious  habit.  One  great  source  of 
gain  in  doing  work  that  is  consecutive  rather  than  broken  and 
fragmentary  work  is  that  in  the  former  the  initial  act  of  the  will 


REUSE 


17 


which  starts  a  piece  of  consecutive  work  does  not  need  to  be 
repeated  but  is,  so  to  speak,  used  repeatedly  and  continuously  till 
the  work  is  ended.  Also  in  the  process  termed  apperception,  new 
phenomena  and  experiences  are  stated  in  terms  of  the  concepts 
or  units  of  knowledge  which  are  already  in  the  mind;  that  is, 
the  latter  units  are  reused  and  the  process  of  learning  is  thereby 
economized. 

Similarly  the  perceptions,  feelings,  thoughts,  and  ideas  of  other 
persons  may  be  reused  by  an  individual.  The  volitions  of  the 
teacher  are  reused  by  a  class ;  those  of  a  general  by  an  army ;  and 
those  of  any  pace  maker  or  leader  by  his  followers. 

Also  larger,  more  objective  and  complex  mental  products  may  be 
and  are  reused  with  fruitages  correspondingly  large  and  high  in 
the  scale  of  values.  Thus  experience,  education,  theories,  hypothe- 
ses, and  systems  of  thought  of  all  kinds  may  be  reused  by  different 
individuals  in  a  great  variety  of  ways.  For  instance  the  alphabet 
has  been  used  by  many  nations  and  generations  besides  its  inventors ; 
and  for  many  purposes  which  its  inventors  did  not  intend,  as  in 
lettering  diagrams  in  mathematics,  or  in  expressing  systems  of 
classification  in  science  and  logic. 

In  certain  aspects  work  or  energy  can  be  reused.  The  savage  in 
using  the  same  club  repeatedly,  reuses  not  only  the  object  itself  but 
also  the  work  done  in  searching  for  the  club  and  in  shaping  it.  This 
principle  applies  in  the  reuse  of  all  tools,  machinery,  and  systems 
of  thought;  to  the  imitation  of  other  persons  and  the  copying  of 
their  work.  In  setting  timepieces  we  reuse  the  work  of  the  astrono- 
mer who  has  accurately  determined  the  time  of  day.  In  riding  on 
a  railroad  we  reuse  the  work  of  the  engineers  and  laborers  who 
constructed  the  road.    Civil  law  is  based  on  the  reuse  of  precedents. 

The  Fuegians  observed  by  Darwin  kept  the  time  of  day,  not  by  a 
clock,  but  by  having  that  old  man  in  their  midst  in  whom  the 
natural  sense  of  time  measurement  was  most  accurate,  strike  a  bell 
at  what  he  judged  to  be  equal  intervals.  In  this  way  the  Fuegians 
reused  the  work  of  nature  in  endowing  this  man  with  peculiar  facul- 
ties and  his  own  work  in  developing  these  faculties.  Similarly  in 
reusing  various  inventions  we  reuse  the  toil,  or  genius,  or  both, 
which  have  made  these  discoveries  and  inventions  possible.  The 
data  thus  reused  become  very  extensive  and  complicated  when  traced 
back  in  all  their  ramifications. 


i8  SOURCES  OF  EFFICIENCY 

Limitations  in  Reuse  of  Objects 

It  should  be  noted  in  this  connection  that  not  all  objects  can  be 
reused,  nor  can  every  object  be  reused  in  all  ways.  If  a  material 
object  has  been  once  used  and  afterward  has  become  inaccessible  in 
time  or  space,  it  cannot  then  be  reused.  Certain  objects  may  be  too 
large,  or  too  small,  or  otherwise  unfit  for  reuse  of  a  given  kind. 
Also  an  object  which  has  been  worn  out,  lost,  or  destroyed  cannot 
be  used  again.  A  ton  of  coal  cannot  be  burned  a  second  time.  A 
system  may  be  beyond  the  comprehension  of  the  person  who  seeks 
to  reuse  it.  In  other  words,  the  repeated  use  of  things  is  often 
prevented  by  subjective  limitations  in  the  user  as  well  as  by  objective 
limitations  in  the  things  themselves.  This  matter  will  be  discussed 
more  fully  in  Chapter  XV  (p.  265). 

Numerical  Forms  of  Reuse 

Instances  of  reuse  may  also  be  classified  according  to  individual 
forms  in  which  they  occur. 

Thus  certain  cases  of  reuse  may  be  characterized  by  a  numerical 
element  prominent  in  them.  For  instance  if  a  single  object  is 
reused,  the  case  may  be  described  as  unitary.  Similarly  if  two, 
three,  or  any  number  of  data  (denoted  as  w  data)  are  reused  in  a 
given  case,  the  process  involved  may  be  termed  dual,  triple,  or 
n-fold  reuse.  Also,  if  a  given  object  is  reused  one,  two,  or  n  times, 
the  corresponding  processes  may  be  denominated  by  a  similar  set 
of  numerical  terms. 

An  important  special  case  under  this  head  may  be  termed  dual 
reciprocal  reuse.  As  an  illustration  we  have  the  fact  that  a  hunter 
reuses  the  power  of  smell  in  his  dog,  while  the  dog  in  effect  reuses 
the  superior  powers  of  vision  and  reasoning  in  the  hunter.  Each 
blade  of  a  pair  of  scissors  reuses  the  other.  Each  of  two  friends 
or  two  partners  in  any  enterprise  repeatedly  uses  the  other. 

If  this  method  of  reuse  be  extended  to  any  number  of  agents 
(that  is,  to  n  agents)  it  becomes  what  may  be  termed  w-reciprocal 
reuse.  Thus  a  set  of  salesmen  may  all  reuse  the  special  devices 
invented  by  any  one  of  the  set.  So  in  any  good  organization,  system, 
society,  or  corporation,  all  the  parts  and  members  reuse  the  good  or 
virtue  in  any  one  part  or  member. 


REUSE  19 

Spatial  Forms  of  Reuse 

Cases  of  reuse  may  also  be  characterized  by  some  spatial  or 
quantitative  element  prominent  in  them.  For  example  different 
kinds  of  reuse  may  be  local  or  comprehensive.  A  process  or  datum 
may  be  reused  in  a  near  field  as  when  the  spectroscope  is  applied  to 
a  new  chemical  substance  in  the  laboratory ;  or  in  a  remote  field,  as 
when  the  spectroscope  is  used  in  studying  the  stars.  So  a  case  of 
reuse  may  be  characterized  by  the  transfer  of  the  reused  material 
from  a  large  domain  to  a  small  one,  as  when  we  use  our  knowledge 
of  the  solar  system  in  explaining  the  constitution  of  a  molecule;  or 
vice  versa. 

Cases  of  reuse  may  also  be  described  as  one,  two,  or  three 
dimensional.  For  instance,  a  travelling  crane  moves  back  and  forth 
in  a  line  (that  is,  along  a  beam),  and  is  usable  in  its  various  posi- 
tions. Hence  this  may  be  described  as  a  case  of  linear  reuse. 
Similarly  we  have  cases  of  circular  and  spiral  reuse,  or  reuse  ex- 
panding from  a  point  in  a  fanshaped,  conical,  or  spherical  way. 

Marginal  Reuse 

Certain  forms  of  the  efficiency  process  under  discussion  may  be 
termed  partial,  differential,  or  marginal  reuse.  Thus  if  an  engineer 
should  want  to  measure  the  distance  from  Washington  to  Albany, 
and  he  already  knew  the  distance  from  Washington  to  New  York, 
he  could  save  himself  labor  by  reusing  his  knowledge  of  the  distance 
from  Washington  to  New  York,  and  measuring  only  the  distance 
from  New  York  to  Albany.  Similarly  the  astronomer  diminishes 
the  work  of  determining  the  position  of  many  stars  and  other  bodies 
on  the  celestial  sphere  by  first  measuring  once  for  all  with  great 
accuracy  the  position  of  certain  fundamental  stars,  and  then  measur- 
ing the  distance  of  other  objects  from  these  primary  stars.  In  doing 
a  large  amount  of  work  in  this  way  the  astronomer  obviously  reuses 
many  times  the  work  done  on  the  fundamental  stars. 

Similarly  in  the  mastery  and  reuse  of  certain  representative  types 
of  organisms  in  biology,  or  of  symbolisms  in  art,  or  of  minds  in 
psychology,  we  are  applying  that  principle  of  efficiency  which  we 
have  termed  marginal  or  variant  reuse.  We  have  an  even  more 
important  case  of  it  in  the  mastery  and  use  of  fundamental  princi- 
ples in  ethics,  religion,  logic,  and  philosophy,  and  then  applying 
with  slight  variations  this  knowledge  in  various  special  fields. 

In  forming  the  plural  of  a  word  by  annexing  the  letter  s  (see 


20  SOURCES  OF  EFFICIENCY 

apples  as  formed  from  apple)  instead  of  forming  an  entirely  new- 
word,  we  save  labor  by  means  of  marginal  reuse.  The  same  eco- 
nomic principle  is  at  work  in  the  use  of  the  various  suffixes,  prefixes, 
and  other  modifiers  of  words  employed  in  language. 

An  application  of  this  principle  in  another  field  is  found  in  the 
use  of  the  so-called  universal  machine;  that  is,  a  machine  which 
by  slight  modifications  of  its  fundamental  framework  or  of  its 
details,  may  be  made  to  do  the  work  of  a  variety  of  distinct 
machines.  A  simple  instance  of  like  nature  is  the  use  of  one  brace 
and  a  number  of  bits  instead  of  several  augers.  A  similar  case  is 
the  use  of  one  tug  boat  and  a  number  of  barges  instead  of  several 
steamboats.  In  a  steamboat  the  engine  must  be  idle  while  the  boat 
is  being  loaded  or  unloaded;  but  in  a  tug  boat  the  engine  may  be 
kept  in  almost  constant  use  in  moving  some  barges  while  others  are 
loading  or  unloading.  Hence  one  engine  in  a  tug  boat  takes  the 
place  of  several  engines  in  steamboats,  or  is  relatively  reused.  If  all 
the  bits  mentioned  above  as  used  with  a  brace  are  replaced  by  a 
single  adjustable  bit,  the  case  becomes  one  of  marginal  reuse  of 
the  second  order.  An  important  special  case  of  marginal  reuse  is 
what  may  be  termed  repair  reuse.  An  instance  of  this  is  replacing 
a  broken  mainspring  in  a  watch  by  a  new  mainspring  instead  of 
buying  a  new  watch;  or  having  a  pair  of  shoes  half-soled  instead  of 
buying  a  new  pair. 

Temporal  Forms  of  Reuse 

With,  respect  to  the  category  of  time  cases  of  reuse  may  be 
characterized  in  a  number  of  ways,  as  for  instance  by  the  adjectives 
temporary  or  permanent.  The  most  important  special  case  in  this 
connection  is  what  may  be  termed  prophetic  or  anticipative  reuse. 
Thus  if  a  man  sees  a  small  leak  in  a  dam  and  stops  it  at  once  by 
wheeling  a  small  barrow  of  dirt  to  it,  his  work  is  reused  in  the  sense 
that  it  is  a  substitute  for  the  much  greater  labor  of  rebuilding  the 
dam  after  it  has  been  swept  away.  Similarly  we  have  the  proverb 
that  a  stitch  in  time  saves  nine.  What  is  called  preventive  medicine 
is  an  instance  of  the  same  sort  of  efficiency.  In  fact  a  large  part  of 
the  virtue  in  farsightedness,  forehandedness,  and  all  wise  planning 
is  of  the  same  kind.  So  also  care  in  laying  a  good  foundation,  or  in 
making  a  good  start,  partakes  of  the  nature  of  prophetic  reuse. 


REUSE  '  21 

Other  Special  Forms  of  Reuse 

Space  and  time  together  give  rise  to  the  idea  of  motion  and  order, 
and  to  corresponding  classes  of  reuse.  Thus  in  the  case  of  a  travel- 
Hng  Hbrary,  the  motion  of  the  books  is  the  means  of  their  repeated 
use,  and  the  reuse  involved  may  be  described  as  motional. 

Reuse  obtained  by  means  of  the  idea  of  order  is  illustrated  by 
the  repeated  use  of  a  road  obtained  by  travelling  over  the  road  in 
opposite  directions,  or  by  the  temporary  conversion  of  a  dynamo 
into  an  electric  motor  by  simply  reversing  its  action. 

When  a  given  object  or  idea  is  propagated,  spreads,  or  grows,  the 
element  of  force  enters  into  the  case  in  a  special  way.  Cases  of 
this  kind  may  perhaps  be  denominated  as  growth  reuse. 

With  respect  to  the  category  of  quality,  instances  of  reuse  may 
be  characterized,  for  example,  as  homogeneous  or  heterogeneous. 
Thus  a  certain  method  of  bracing  the  framework  of  bridges  having 
been  invented,  so  long  as  it  was  reused  in  this  kind  of  work  only,  it 
constituted  a  case  of  homogeneous  reuse.  When  it  was  later  used 
in  making  the  framework  of  freight  cars,  it  became  a  case  of  hetero- 
geneous reuse.  Almost  all  schoolhouses  were  originally  built  as 
places  to  be  used  exclusively  for  the  training  of  children.  Recently 
many  such  buildings  have  come  to  be  used  by  adults  also  for  various 
social  and  cultural  purposes,  this  latter  application  being  a  case  of 
heterogeneous  reuse.  Mr.  Westinghouse  having  invented  a  system 
of  economical  transmission  of  gas  by  high  pressure  mains,  reused 
this  principle  in  devising  an  economical  method  of  transmitting 
electricity  by  means  of  high  voltages  on  the  principal  wires.  This 
also  is  evidently  a  case  of  heterogeneous  reuse. 

Heterogeneous  reuse  may  also  be  regarded  as  a  kind  of  qualitative 
marginal  reuse. 

Negative  Reuse 

In  this  connection  should  be  mentioned  what  may  be  termed 
negative  reuse.  An  instance  of  this  is  learning  from  the  results  of  a 
mistake  not  to  repeat  the  error.  Another  form  of  negative  reuse  is 
that  in  which,  having  learned  an  exclusive  property  of  an  object  or 
group  of  objects,  we  infer  the  opposite  or  negative  of  this  property 
for  other  objects.  This  form  of  reuse  is  useful  in  some  varieties 
of  proof,  in  detective  work,  and  in  certain  kinds  of  scientific  in- 
vestigation. 


22  SOURCES  OF  EFFICIENCY 

Scales  af  Reuse 

It  is  also  important  to  observe  that  species  of  reuse  may  be 
arranged  according  to  a  certain  scale  of  value.  Thus  the  reuse  of 
one's  powers  of  invention  and  discovery  is  a  higher  kind  of  effi- 
ciency than  copying  or  imitating  the  work  of  another  person  directly. 
When  fire  was  first  discovered,  it  was  an  economy  for  man  to  reuse 
it  by  keeping  it  from  going  out  and  by  transferring  it  from  place  to 
place.  But  later,  noticeably  after  the  invention  of  the  lucifer  match, 
man  substituted  for  the  reuse  of  fire  once  made,  the  higher  reuse  of 
work  done  by  the  inventor  of  the  match  and  by  other  scientific  work- 
ers. A  still  more  general  case  of  highly  important  repeated  use  is 
reuse  of  reuse.  Thus  when  a  farmer  after  reusing  the  methods  of  a 
government  expert  in  raising  corn  and  finding  them  profitable, 
later  reuses  the  methods  of  other  experts  in  raising  cotton,  wheat, 
clover,  etc.,  he  practises  reuse  of  reuse,  or  reuse  of  the  second  order. 
In  general,  from  our  point  of  view,  repeated  use  of  the  primal  agen- 
cies of  efficiency  now  under  investigation  is  reuse  of  the  highest 
order. 

Obscure  Cases 

Certain  cases  of  more  or  less  obscure  reuse  should  be  mentioned. 
These  are  illustrated  by  the  action  of  enzymes  and  catalysts  in 
chemistry.  For  example  the  presence  of  a  plate  of  platinum  greatly 
accelerates  the  combination  of  oxygen  and  hydrogen  to  form  water. 
This  action  takes  place  without  any  noticeable  change  in  the  plat- 
inum plate.  Hence  the  plate  can  be  reused  indefinitely  for  the  pur- 
pose mentioned.  The  fact  is  plain  but  the  nature  of  the  process 
involved  is  obscure.  Other  cases  of  like  nature  are  regarded  as  less 
obscure  only  because  they  are  more  familiar.  In  this  connection  may 
be  mentioned  the  repetition  in  nature  of  like  forms  such  as  atoms, 
molecules,  cells,  crystals,  and  organisms,  and  of  the  qualities  of 
parents  in  their  offspring,  often  after  a  number  of  generations  in 
which  the  given  qualities  have  not  been  present. 

Another  case  of  partially  obscure  reuse  is  that  which  is  often 
called  influence.  Examples  of  this  are  the  effect  of  a  large  and 
efficient  army  in  preserving  peace,  of  a  reserve  of  capital  in  pre- 
venting a  panic,  or  many  of  the  changes  wrought  in  a  community 
by  the  mere  presence  in  it  of  a  strong  personality. 


REUSE  23 

Complex  and  other  Forms  of  Reuse 

Other  species  of  reuse  might  be  characterized  as  conscious  or 
unconscious,  swift  or  slow,  feeble,  automatic,  or  irresistible,  but  it 
does  not  seem  necessary  to  examine  these  and  like  cases  in  detail. 
In  concluding  the  topic  of  classification  of  cases  of  reuse,  special 
mention  should  be  made  of  compound  and  complex  forms.  An 
illustration  is  the  case  of  a  soldier  discharging  his  gun.  In  doing 
so  he  reuses  the  metal  in  the  gun,  the  wisdom  of  his  general,  the 
work  of  scouts  and  officers,  the  work  of  drill,  and  the  labor  of 
men  who  invented  the  use  of  metals  and  gunpowder,  and  much 
more  implied  by  these  items  and  also  outside  of  them.  An  evea 
more  complex  case  is  the  reuse  of  western  civilization,  for  instance,, 
by  the  Japanese.  Looked  at  from  another  point  of  view,  a  single 
act  of  reuse  may  involve  not  only  the  repeated  use  of  many  differ- 
ent objects  and  kinds  of  work,  but  also  a  variety  of  forms  of  reuse> 
as  those  which  have  been  named  plural,  prophetic,  fanshaped,, 
heterogeneous,  and  unconscious. 

ADVANTAGES   IN   REUSE 

Economics  due  to  Reuse 

We  shall  next  consider  the  advantages  in  reuse  as  a  source  of 
efficiency.  Some  of  these  benefits  are  so  obvious  as  to  need  no  ex- 
tended discussion.  Among  these  are  economy  of  material,  and 
hence  of  money  and  other  resources.  Thus  if  a  manufacturer 
instead  of  building  an  additional  factory  uses  his  old  factory  by 
night  as  well  as  by  day,  he  saves  the  cost  of  the  new  building,  of. 
ground  on  which  to  place  it,  of  taxes,  repairs,  watchmen,  and 
insurance. 

In  like  manner  repeated  use  means  a  saving  of  time  and  strength, 
and  thus,  in  effect,  gives  new  strength,  and  lengthens  and  enlarges, 
life. 

Added  Power 

Other  advantages,  not  always  so  obvious  as  the  above,  often  ap^ 
pear  in  connection  with  reuse.  Thus  economy  of  resources  sets 
free  certain  powers,  often  higher  powers,  in  the  reuser,  to  be  em- 
ployed in  more  efficient  ways  than  reuse  itself.  These  methods  wilt; 
be  indicated  more  definitely  in  later  chapters. 


24  SOURCES  OF  EFFICIENCY 

Infinite  Value  in  Reuse 

Special  mention  should  be  made  of  the  absolute,  or  relatively 
infinite  gain  which  sometimes  results  from  reuse,  as  when  it  enables 
a  person  to  overcome  an  otherwise  insuperable  difficulty.  Thus  if  a 
man  wishes  to  carry  to  the  top  of  a  hill  a  rock  which  is  too  large  for 
him  to  manage  as  a  whole,  he  may  often  accomplish  his  purpose  by 
breaking  the  rock  to  pieces  and  carrying  it  up  the  hill  piecemeal  by 
reuse  of  his  powers.  Similarly,  the  lever,  pulley,  inclined  plane, 
and  like  mechanical  devices  often  enable  us  to  achieve  otherwise 
impossible  results.  A  realization  of  the  general  value  of  this  princi- 
ple of  efficiency  is  expressed  in  the  proverb  "Divide  and  conquer". 

Other  Values 

In  some  cases  reuse  gives  beneficial  results  which  are  obvious  but 
which  are  difficult  fully  to  analyze,  either  on  account  of  their  com- 
plexity or  for  other  reasons.  Thus  reuse  of  a  scaffolding  in  a 
sense  produces  the  building.  The  inertia  or  persistence  reuse  of 
each  of  a  set  of  pictures  on  the  retina  or  in  the  brain  gives  the 
result  called  the- moving  picture. 

As  a  more  abstract  illustration  of  the  species  of  efficiency  function 
under  consideration  we  have  the  method  of  proof  called  mathemat- 
ical induction.  In  this  form  of  proof,  a  unit  step  of  reasoning  is 
first  demonstrated,  and  then  reused  an  unlimited  number  of  times, 
and  a  final  result  thus  obtained,  often  apparently  not  demonstrable 
in  any  other  way. 

Reuse  Greater  in  Higher  Organisms 

It  may  be  well  also  to  look  at  the  advantages  of  reuse  in  a 
collective,  historical,  and,  in  a  sense,  pictorial  way. 

If  we  examine  the  forms  of  animal  life,  as  we  proceed  from  lower 
to  higher  forms,  we  find  a  progressive  increase  in  the  amount  of 
reuse  and  in  the  elevation  of  the  character  of  reuse.  In  fact  the 
extent  and  quality  of  repeated  use  practised  by  an  organism  may  be 
said  to  form  a  measure  or  test  of  the  place  of  the  organism  in  the 
scale  of  life. 

Thus  if  we  first  consider  subjective  reuse,  that  is,  the  reuse  of 
parts  or  members  of  itself  by  an  object,  we  find  that  a  lower 
organism  such  as  the  amoeba,  while  it  of  course  reuses  its  own 
substance,  often  does  not  reuse  forms  or  structures  of  this  substance. 


REUSE  25 

On  the  contrary,  as  has  been  already  pointed  out,  it  improvises  a 
new  arm  or  mouth  whenever  the  need  for  such  arises.  On  the 
other  hand,  it  is  the  rule  for  a  higher  organism  to  reuse  its  limbs 
and  organs.  In  man  this  reuse  of  the  physique  or  body  is  sur- 
rounded by  and  included  in  a  still  higher  class  of  reuse,  viz. :  that 
of  certain  mental  powers. 

If  we  next  consider  objective  reuse,  that  is,  the  reuse  by  an 
organism  of  objects  outside  of  itself,  we  find  that  the  same  law 
holds ;  that  is,  the  higher  the  organism  in  the  scale  of  life,  the  more 
extended  in  both  time  and  space  is  the  reuse  practised  by  it,  and  the 
higher  is  the  order  of  this  reuse.  Thus  the  spider  reuses  its  web 
for  but  a  few  days.  Man  reuses  his  houses  and  railroads  for  many 
years;  and  he  reuses  systems  and  theories  which  are  entirely  above 
and  beyond  the  world  of  the  spider  and  of  lower  organisms  in 
general. 

High  Degree  of  Reuse  in  Great  Men 

We  find  also  that  the  greatest  men  and  the  greatest  nations  have 
been  the  greatest  reusers.  Newton  said  he  had  been  able  to  accom- 
plish what  he  did  because  he  stood  on  the  shoulders  of  giants. 
Shakespeare  freely  reused  the  forms  of  ancient  art,  plots  and 
stories,  preceding  philosophies  as  summed  up  by  Montaigne,  Chris- 
tianity, and  all  the  current  thought  and  discoveries  of  his  own  age. 
In  fact  it  has  been  laid  down  as  a  law  that  "men  of  the  largest 
original  power  make  the  most  use  of  the  results  obtained  by  other 
men". 

What  we  regard  as  the  sudden  and  miraculous  manifestations 
of  genius  are  often,  and  perhaps  always  in  some  respect,  the  unob- 
served accumulations  of  acts  of  reuse.  Thus  the  marvellous  pro- 
ducts of  Greek  sculpture  were  in  large  part  due  to  many  generations 
of  Greek  workmen  and  artists,  each  generation  using  what  the  pre- 
ceding ones  had  learned,  and  each  adding  its  own  contribution  to 
artistic  tradition. 

Departments  of  Knowledge  Based  on  Reuse 

If  we  look  at  the  matter  from  another  point  of  view,  each  depart- 
ment of  human  activity  or  thought  is  found  to  have  at  its  foun- 
dation certain  elements  or  units  which  are  reused  in  certain 
characteristic  and  systematic  ways.  The  fruitage  of  the  entire  body 
of  reuse  in  each  case  is  so  great  as  to  make  it  an  advantage  to  mark 


26  SOURCES  OF  EFFICIENCY 

off  each  aggregate  and  its  possible  future  developments,  as  a 
separate  domain  of  knowledge  or  life. 

For  instance,  the  existence  of  trigonometry  as  a  distinct  branch 
of  mathematics  is  due  to  the  fact  that  certain  men  once  calculated 
certain  numerical  tables,  and  that  other  men  in  using  these  tables 
have  reused  and  got  for  nothing  the  work  done  by  these  computers. 
Also  the  tables  having  been  computed,  men  using  them  found  it  an 
advantage  to  give  characteristic  names  to  the  functions  represented 
in  the  tables,  later  to  denote  these  functions  by  specific  symbols,  and 
by  the  aid  of  these  symbols  to  build  up  an  extensive  system  of  rela- 
tions among  the  concepts  thus  treated.  In  a  word,  a  simple  system 
of  reuse  developed  into  an  extensive  yet  definite  domain  of  economic 
and  efficient  relations. 

In  this  connection  it  should  be  noted  that  every  great  invention 
or  idea,  almost  without  exception,  at  first  occurred  to  its  originator 
in  some  special  or  individual  form,  and  was  afterward  developed  by 
various  kinds  of  reuse  into  a  more  general  form. 

Functional  Foremen 

At  present  in  many  lines  of  business  the  realization  of  the  value  of 
reuse  is  increasing.  Thus  in  F.  W.  Taylor's  system  of  conducting 
business,  called  scientific  management,  it  is  proposed  to  observe  or 
work  out  the  best  method  of  performing  every  item  of  work,  and  to 
have  so-called  functional  foremen  appointed  so  that  by  them  each 
workman  can  be  thoroughly  instructed  in  the  methods  thus  worked 
out. 

Loss  due  to  Absence  of  Reuse 

Another  method  by  which  to  grasp  the  importance  of  the  princi- 
ple of  reuse  in  human  life  is  to  try  to  realize  what  existence  would 
become  if  this  method  of  obtaining  results  were  eliminated.  Thus, 
in  the  individual  life,  actions  like  walking,  breathing,  and  the  use 
of  memory  would  cease.  In  the  relations  of  individuals,  a  large  part 
of  what  goes  by  the  name  of  co-operation,  as  well  as  all  use  of  the 
work  done  by  one's  predecessors,  expanding  as  it  does  into  a  remote 
past,  would  be  cancelled. 

As  we  study  other  primal  efficiency  principles  in  succeeding  chap- 
ters, we  shall  find  that  reuse  has  additional  important  uses  in  con- 
nection with  these  principles. 


REUSE  27 

Definition  of  Reuse 

It  may  be  well  at  this  point  to  define  the  term  reuse  as  clearly  as 
possible. 

To  use  an  object  means  to  combine  the  given  object  with  other 
objects  so  as  to  produce  results  of  value  (a  surplusage  or  positive 
non-equivalence:  see  Chapter  IX,  p.  152). 

To  reuse  an  object  means  to  repeat  the  process  of  use  in  whole 
or  part. 

METHODS  OF  APPLICATION 

We  shall  now  consider  the  most  efficient  methods  of  applying  the 
principle  of  reuse. 

Vast  Number  of  Species  of  Reuse 

In  order  to  reap  the  largest  possible  benefit  from  the  employment 
of  this  principle  of  efficiency  it  is  important  to  consider  it  first  with 
reference  to  the  category  of  number ;  that  is,  to  realize 

( 1 )  The  vast  number  of  objects  and  entities  which  may  be  reused ; 

(2)  The  vast  variety  of  forms  which  each  species  of  reuse  may 

assume; 

(3)  The  great  number  of  elements  which  may  enter  into  a  seem- 

ingly simple  act  of  reuse. 

A  mastery  of  the  category  of  space  also  aids  in  the  extended  and 
improved  use  of  the  principle  of  efficiency  under  consideration. 
For  instance  such  mastery  aids  in  learning  to  reuse  data  in  widely 
separated  domains;  in  realizing  the  various  spatial  ways  in  which 
reuse  may  spread;  and  in  determining  which  of  these  forms  will 
be  most  effective  in  a  given  case. 

Possible  Extent  of  Reuse 

It  is  also  important  in  this  connection  to  realize  the  extent  to 
which  reuse  may  be  carried.  Thus,  in  the  department  of  scientific 
work  alone,  it  is  estimated  that  10,000  men  of  substantial  ability  are 
at  work  making  original  researches,  and  that  each  volume  of  a 
scientific  journal  contains  the  results  of  100,000  brain-power  hours 
of  work.  All  of  these  results  are  available  for  each  and  every 
worker  as  material  of  reuse. 


28  SOURCES  OF  EFFICIENCY 

Reuse  increased  by  Auxiliary  Objects 

Of  high  importance  also  is  the  study  of  the  use  of  auxiliary  ob- 
jects in  connection  with  reuse  (see  Chapter  VII,  p.  iii).  Thus 
paper,  ink,  and  language,  as  used  in  making  permanent  records  of 
otherwise  transitory  material,  are  important  aids  in  the  reuse  of 
ideas  and  experience.  Buildings  in  which  books  can  be  stored  are 
a  farther  aid  to  the  extended  reuse  of  the  facts  and  ideas  recorded 
in  books.  If  the  books  are  occasionally  sent  out  in  travelling  libra- 
ries, railroads  and  the  forces  which  operate  railroads  may  also  be 
regarded  as  agencies  auxiliary  to  repeated  use.  Paint  on  a  house 
preserves  the  house  and  thus  leads  to  the  continued  use  of  the  house 
long  after  it  would  otherwise  have  perished.  A  servant  by  means  of 
a  letter  is  enabled  to  reuse  or  get  advantage  from  work  done  in  a 
previous  situation.  Photographs  are  aids  to  reuse  in  many  evident 
ways. 

A  more  abstract  form  of  auxiliary  entity  is  an  extended  view  of 
things  as  an  aid  in  selecting  the  best  material  or  devising  the  most 
efficient  units  and  methods  of  reuse  in  a  given  case.  A  wide  outlook 
gives  a  greater  variety  of  material  to  select  from,  and  thus  opens 
the  way  to  the  utilization  of  more  efficient  data  and  methods  of 
reuse. 

By  the  use  of  auxiliaries  certain  limitations  in  reuse  may  often 
be  overcome.  Thus  a  ton  of  coal  cannot  be  burned  a  second  time, 
but  the  heat  generated  in  burning  the  coal  may  be  used  to  make 
a  machine  which  may  be  reused  many  times,  or  to  sustain  a  think- 
ing person  whose  thought  product  may  be  reused  and  expanded 
indefinitely. 

Reuse  of  the  Best  Materials 

This  leads  us  to  the  question  as  to  what  are  the  most  efficient 
kinds  of  reuse.  Many  elements  enter  into  a  solution  of  this  problem. 
We  can  here  mention  only  a  few  of  the  more  important.  Among 
the  best  data  for  reuse  purposes  are  those  which  are  most  accurate, 
have  been  most  thoroughly  tested,  or  are  most  finished  or  perfected 
in  any  way.  In  other  words,  whatever  we  do  or  make  it  pays  to  do 
in  such  a  way  that  the  results  obtained  shall  be  reusable.  Hence  the 
proverb  that  whatever  is  worth  doing  at  all  is  worth  doing  well,  here 
receives  a  new  illumination.  Thus  the  best  plays,  like  Shakespeare's, 
are  reused  most  extensively,  especially  if  we  consider  the  higher 
quality  of  the  hearers  of  such  plays  and  the  large  amount  of  indirect 


REUSE  29 

reuse  that  follows  from  this  fact.  The  best  books  live  and  continue 
to  be  reused;  so  of  the  best  scientific  work,  poKtical  work,  and  work 
of  any  kind. 

If  a  work  of  art  be  of  a  high  order,  it  will  be  reused  not  only 
frequently  but  in  a  great  variety  of  ways  as  by  copies,  photographs, 
and  variations.  The  same  law  holds  for  any  unusually  meritorious 
product.  Such  work  will  also  be  reused  with  great  speed  and  ease. 
The  Arabic  system  of  Arithmetic  was  introduced  into  Europe  about 
the  year  1200  A.D.  It  was  so  superior  to  the  Roman  system  that, 
notwithstanding  the  primitive  state  of  culture  of  that  time,  it  spread 
rapidly  and  practically  without  opposition  from  land  to  land.  So 
smooth  and  rapid  was  the  transition  that  it  is  almost  impossible  to 
trace  its  stages. 

To  give  a  negative  illustration  of  the  principle  under  discussion, 
the  Chinese  alphabet  is  so  crude  and  the  characters  composing  it 
capable  of  so  little  reuse  and  therefore  so  numerous  that  it  is  esti- 
mated that  a  Chinese  compositor  walks  20  miles  a  day  in  setting  up 
type,  while  a  compositor  in  the  English  language  may  remain  in  a 
practically  stationary  position. 

Highest  Forms  of  Reuse 

The  most  efficient  cases  of  reuse  imply  not  only  material  but  also 
forms  of  a  high  order.  Thus  imitation  is  usually  a  low  form  of  re- 
peated use  and  often  detrimental  in  many  of  its  results,  while 
prophetic  reuse  is  almost  invariably  highly  valuable.  Reuse  of  reuse 
is  also  one  of  the  highest  forms  of  this  source  of  efficiency.  For 
example,  if  a  particular  instance  of  reuse  of  any  kind  has  been 
observed,  it  is  frequently  a  highly  efficient  process  to  reuse  this 
reuse  in  other  domains.  Thus  after  it  had  been  observed  that 
germs  of  certain  diseases  travelled  by  the  reuse  of  the  motion  of  one 
insect,  as  the  mosquito,  it  might  at  once  have  been  inferred  that  other 
germs  travel  by  other  insects  as  ticks,  fleas,  and  flies,  and  investi- 
gations made  accordingly. 

Often  it  is  profitable  to  start  with  a  low  order  of  reuse  and  de- 
velop it  step  by  step  into  a  higher  order.  Thus  in  teaching  geogra- 
phy it  is  usually  best  to  have  the  pupil  begin  with  the  study  of  his 
local  surroundings  and  to  reuse  these  till  he  forms  general  concep- 
tions of  the  earth  as  a  whole  which  he  can  then  reuse  deductively. 
So  in  general  it  is  often  well  to  begin  with  psychological  or  inductive 
reuse  and  develop  it  into  the  more  rapid  and  powerful  logical  and 
deductive  reuse. 


30  SOURCES  OF  EFFICIENCY 

Limitations  in  Reuse 

Of  highest  importance  in  the  practical  application  of  reuse  is  the 
study  of  the  limitations  connected  with  it.  Every  source  of  effi- 
ciency is  hedged  in  by  characteristic  restrictions.  Thus  in  the  case 
in  hand  the  materials  capable  of  reuse  are  limited  in  certain  ways 
some  of  which  have  been  indicated  on  a  previous  page.  Similarly 
the  forms  of  reuse  are  limited.  More  specifically,  a  given  material 
is  capable  of  only  certain  special  forms  of  reuse.  Also  each  form  or 
kind  of  reuse  brings  its  own  limitations.  Repeated  use  is  also 
hedged  in  by  certain  deficiencies  in  the  persons  or  agencies  which 
attempt  to  carry  out  the  process  involved. 

Adaptation  in  the  Application  of  Reuse 

Hence  in  many  cases  much  study  is  necessary  in  order  to  deter- 
mine that  particular  species  of  reuse  which  it  is  most  advantageous 
to  employ  in  a  given  case,  or  whether  indeed  it  may  not  be  better 
to  employ  some  other  prime  agent  of  efficiency.  Thus  imitation  is 
one  of  the  simplest  and  easiest  forms  of  reuse,  but  it  often  tends  to 
an  atrophy  of  reuse  processes  of  a  higher  kind,  as  of  powers  of 
invention  and  discovery.  Just  as  the  tape  worm,  living  directly  on 
another  organism,  has  neither  mouth  nor  digestive  tract  so  the  mere 
imitator  loses  the  powers  of  invention  and  initiative. 

Herbert  Spencer  reused  the  principles  of  biology  in  the  field 
of  psychology  with  good  results,  but  when  he  applied  the  same 
principles  in  sociology,  the  results  were  misleading  rather  than 
illuminating. 

Similarly  different  kinds  of  reuse  wax  in  value  or  lapse  into 
danger  with  changing  circumstances.  Marginal  reuse  is  particularly 
variable  in  this  respect.  In  a  multitude  of  cases  where  its  applica- 
tion is  possible,  it  is  necessary  to  determine  whether  it  will  pay  best 
to  repair  an  object  or  to  procure  a  new  one;  that  is,  whether  to 
mend  or  end  the  object. 

One  of  the  best  ways  in  which  to  avoid  the  limitations  and  evils 
of  reuse  of  a  low  order  is  to  use  such  forms  of  reuse  in  combination 
with  reuse  processes  of  higher  order,  or  indeed  with  other  of  the 
primal  sources  of  efficiency.  For  example  in  undertaking  any  spe- 
cific investigation  it  is  of  the  utmost  importance  to  learn  at  the 
outset  what  other  workers  in  the  same  line  have  accomplished. 
These  results  can  be  reused  with  the  utmost  freedom  and  without 


REUSE 


31 


any  ill  effect  (rather  with  multiplied  benefit)   if  at  the  same  time 
we  reuse  our  higher  powers  of  invention  and  adaptation. 

If  we  surround  direct  concrete  reuse  with  other  reuse  of  higher 
orders,  the  more  of  the  former  the  better.  As  a  result  of  this  free 
combination  of  different  orders  of  the  principle  in  hand,  many  of 
the  processes  involved  will  in  time  become  automatic  and  instinctive 
(and  at  the  same  time  in  a  sense  hyper-rational). 

Ideal  Species  of  Reuse 

In  conclusion  it  may  be  well  to  state  that  the  final  and  inclusive 
method  of  applying  this  principle  is  to  reuse  the  most  efficient  mater- 
ials in  the  most  efficient  way  for  the  most  efficient  ends.  In  order 
to  reduce  this  ideal  to  definite  form  under  any  given  circumstances 
a  knowledge  of  other  primal  principles  as  given  in  the  chapters 
which  follow  will  be  useful  and,  indeed,  necessary. 

Summary  of  Chapter 

The  substance  of  the  preceding  chapter  may  be  summed  up  as 
follows:  The  most  primitive  and,  in  a  sense,  fundamental  source 
of  efficiency  is  the  act  of  reuse  or  repetition.  Reuse  takes  many 
special  forms,  each  of  which  has  a  wide  variety  of  applications,  both 
in  the  daily  detailed  life  of  the  individual,  and  in  elaborate  systems. 
Among  the  most  important  individual  forms  of  reuse  are  those 
which  have  been  termed  marginal,  prophetic,  and  reciprocal. 

Reuse  means  not  only  economy  of  material  and  effort,  but  also  *^' 
new  and  aggressive  power.  Often  this  new  power  is  infinite  or  un- 
limited in  nature,  in  that  it  produces  an  advantageous  result  not 
otherwise  obtainable.  The  value  of  reuse  is  also  shown  by  the  fact 
that  the  higher  the  organism,  or  the  greater  the  man,  the  greater 
is  the  power  of  reuse.  So  human  progress  in  general  is  marked  by  :, 
an  increasing  amount  and  by  higher  forms  of  reuse. 

In  order  to  obtain  the  utmost  results  in  the  application  of  reuse, 
it  is  important  to  realize  the  vast  number  of  possible  species  of 
reuse,  to  select  or  devise  the  best  adapted  form  in  each  application, 
and  to  perfect  every  product  of  one's  work  so  that  it  shall  be 
capable  of  the  utmost  reuse.  The  highest  form  of  reuse  is  reuse 
of  the  fundamental  agencies  of  efficiency. 


7^2  SOURCES  OF  EFFICIENCY 

EXERCISE  2 

Give  an  example*  of  reuse  of 

I.  An   inorganic   object  2.  An   idea  3.  An    act   of    volition 

4.  Name  an  object  which  cannot  be  reused  in  a  specified  way. 

5.  Give  an  example  of  dual  reuse. 

6.  Of  reuse  indefinite  with  respect  to  the  number  of  repetitions. 

Give  an  illustration  of  each  of  the  following  species  of  reuse : 

7.  One    dimensional  10.  Reciprocal  13.  Negative 

8.  Two  dimensional  11.  Prophetic  14.  Obtained  by  motion 

9.  Marginal  12.  Growth 

15.  Give  two  related  cases  of  reuse  one  of  which  is  of  low  and  the  other  of 
higher    order. 

Name  the  form  of  reuse  in  each  of  the  following: 

16.  Killing  weeds  before  they   come  up. 

17.  Use  of  a  portable  garage. 

18.  Of  a  bedroom  bureau  convertible  into  a  writing  desk. 

19.  Of  the  word  apples  as  the  plural  of  apple. 

20.  Of  the  results  obtained  at  a  government  agriculture  experiment  station. 

21.  Symbiosis    (or  commensalism)   in  biology. 

22.  The  law  observed  in  old  China  that  "if  any  official  thinks  that  a  custom 
generally  observed  in  his  province  might  with  advantage  be  used  in  the 
while  country"  he  is  to  send  an  account  of  it  to  the  central  government  so 
that  it  can  be  utilized  by  other  provinces. 

23.  A  given  Morris  chair  is  adjustable  at  four  different  angles.  Hence  it 
will  take  the  place  of  how  many  different  chairs  so  far  as  the  resting  of  a 
single  person  is  concerned? 

What  is  its  degree  of  efficiency  in  this  respect? 
What  form  of  reuse  is  involved  in  this  instance? 

24.  A  given  pair  of  gloves  when  mended  at  a  cost  of  10  cents  will  last  half 
as  long  as  a  new  pair  which  will  cost  $1.10.  Determine  the  degree  of  efficiency 
in  mending  and  using  the  old  pair.    What  form  of  reuse  is  here  involved? 

Give  an  illustration  where  reuse  results  in 

25.  Economy  of  material. 

26.  A    saving  of  time   and   strength. 

27.  Attainment  of  a   result  otherwise   impossible. 

28.  How  is  an  envelope  with  a  transparent  front  a  means  of  reuse  to  a 
business  man? 

29.  State  some  of  the  advantages  in  a  son's  learning  and  following  his 
father's  business.     Some  of  the  disadvantages. 

30.  Specify  the  different  items  and  species  of  reuse  involved  in  the  use  of 
the  graphophone. 

*  By  "example",  as  thus  called  for,  is  meant  one  that  is  different  from  those 
already  cited  in  the  text. 


REUSE 


33 


31.  State  the  advantages  in  the  use  of  a  universal  machine.  The  disad- 
vantages. 

32.  Name  the  different  kinds  of  reuse  possible  in  a  large  corporation.  How 
do  these  differ  from  the  forms  of  reuse  possible  in  a  private  firm? 

33.  Give  an  example  where  reuse  otherwise  impossible  is  obtained  by 
means  of  an  auxiliary  object. 

34.  Give  an  instance  where  reuse  produces  loss  of  some  kind. 

35.  A  universal  machine  which  occupies  40  square  feet  of  floor  space  takes 
the  place  of  five  other  machines  which  would  occupy  25,  30,  20,  18,  and  32 
square  feet  respectively.  Compute  the  degree  of  space  efficiency  in  using  the 
universal   machine. 

36.  How  many  items  of  reuse  occur  in  one  application  of  the  principle 
"things  equal  to  the  same  thing  are  equal  to  each  other"? 

37.  Show  in  what  way  logical  deduction  from  general  facts  is  marginal 
reuse.    Illustrate. 

38.  Define  imitation  as  a  special  form  of  reuse. 

39.  The  solar  calendar  originated  in  Egypt.  Trace  the  reuse  of  this 
calendar. 

40.  Discuss  the  meaning  and  functions  of  analogy  as  a  kind  of  reuse. 


CHAPTER  III 

THE  UNIT  AND  ITS  MULTIPLIER 

Illustrations  of  Manifold  Use 

Efficiency  is  sometimes  obtained  by  using  an  object  many  times 
simultaneously  instead  of  many  times  in  succession.  This  process 
differs  from  reuse  in  being  manifold  in  space  instead  of  manifold  in 
time.  Thus  if  a  book  is  taken  from  a  library  by  several  persons  in 
succession  and  read  by  each  of  them,  the  book  is  said  to  be  reused. 
But  if  the  book  is  taken  out  but  once  and  read  aloud  to  a  company 
of  people,  we  have  a  case  of  simultaneous  manifold  use,  or,  more 
briefly,  of  manifold  use.  Other  illustrations  of  simultaneous  mani- 
fold use  are  the  publication  of  an  article  in  several  newspapers  at 
the  same  time  by  a  press  syndicate;  the  cutting  of  several  coats  or 
other  garments  simultaneously  by  the  use  of  a  machine;  duplex,  or 
sextuple  telegraphy  whereby  a  number  of  messages  are  sent  over  a 
wire  at  the  same  time;  the  substitution  of  "J^^^^s  and  John  swam" 
for  "J^^^s  swam  and  John  swam",  the  word  swam  in  the  former 
expression  being  put  to  a  double  use. 

Illustrations  of  Multuse 

By  combining  the  principle  of  successive  use  in  time  with  that  of 
manifold  use  in  space  we  arrive  at  a  principle  more  general  than 
either  of  these  efficiency  processes,  and  including  each  of  them  as  a 
special  case.  Thus  if  a  book  is  taken  from  a  library  repeatedly  and 
each  time  is  read  to  a  different  audience,  the  use  of  the  book  is 
manifold  in  both  time  and  space,  and  we  shall  have  what  may  be 
termed  multuse.  Other  illustrations  of  multuse  are  a  speech  re- 
peated to  several  successive  audiences ;  a  painting  exhibited  several 
times  and  on  each  occasion  viewed  by  a  different  and  often  changing 
group  of  people;  a  school  building  used  not  merely  for  the  instruc- 
tion of  children  but  for  various  social  and  cultural  purposes  on 
successive  occasions  by  the  community  as  a  whole ;  the  imitation  of  a 
model  farm  or  of  a  piece  of  model  road  by  different  sets  of  men; 
the  various  uses  of  the  alphabet  after  it  had  once  been  invented. 
Evidently  the  list  of  such  illustrations  may  be  enlarged  without 
limit. 

34 


UNIT  AND  MULTIPLIER  35 

Manifold  use  and  multuse  are  so  similar  to  reuse  that  they  do 
not  seem  to  need  any  special  treatment  apart  from  that  given  inci- 
dentally in  the  remainder  of  this  chapter. 

Illustration  of  a  Unit  and  its  Multiplier 

A  still  more  comprehensive  principle  of  efficiency  than  any  that 
has  yet  been  mentioned  is  that  of  the  unit  and  its  multiplier.  This 
source  of  efficiency  includes  reuse,  manifold  use,  and  multuse,  as 
special  cases,  and  also  has  characteristic  efficiencies  of  its  own.  For 
instance  if  the  book  mentioned  above  as  taken  from  the  library, 
contains  a  certain  important  idea  this  idea  may  be  regarded  as  a 
unit.  Then  the  number  of  uses  of  this  idea  by  the  reader  of 
the  book,  or  which  follow  directly  or  indirectly  from  such  reading, 
may  be  regarded  as  the  multiplier  of  the  specified  unit.  This  mode 
of  viewing  the  matter  has  the  advantage  of  enabling  us  to  drop  for 
the  time  being  all  the  processes  of  transmission  between  the  datum 
and  the  result  and  freely  to  use  the  datum  and  its  result  in  ways  to 
be  pointed  out  later. 

Other  Advantages  in  the  Unit  and  Multiplier 

The  unit  used  with  a  multiplier  as  a  source  of  efficiency  also  has 
certain  other  characteristic  advantages.  Thus  both  reuse  and  mult- 
use include  or  imply  the  element  of  personality  in  two  ways,  (i) 
They  imply  a  user  or  actor.  (2)  They  imply  an  aim  or  end,  and  a 
person  enjoying  this  aim  or  end  when  attained.  In  the  idea  of  the 
unit  and  multiplier  we  set  aside,  in  a  measure,  this  idea  of  person- 
ality, and  thus  free  ourselves  from  the  caprices,  limitations,  and 
various  entanglements  inherent  in  it.  We  are  thus  enabled,  for 
instance,  to  put  in  the  forefront  objective  and  quantitative  elements, 
and  to  shape  and  adjust  these  to  meet  given  aims  and  needs.  Also 
we  are  set  free  to  expand  the  application  of  a  given  case  without 
limit  in  many  respects.  In  a  word  in  the  unit  and  multiplier  we  have 
the  category  of  multuse  in  a  more  general,  objective,  and  manifold 
form. 

Looked  at  from  another  standpoint,  in  reuse  the  normal  method 
is  to  take  the  data  material  of  reuse  as  we  find  them  and  to  let  the 
methods  and  results  of  the  process  depend  upon  or  follow  from  the 
natural  qualities  of  the  material.  But  in  the  use  of  the  unit  and 
multiplier  we  have  much  greater  freedom.  Because  of  the  some- 
what abstract  nature  of  both  the  unit  and  multiplier  we  may  often 


36  SOURCES  OF  EFFICIENCY 

create  more  or  less  artificial  units  which  will  meet  given  ends  or 
needs  in  a  more  effective  way  than  will  natural  data.  Thus  in  a 
primitive  stage  of  human  development,  the  length  of  the  human 
foot,  or  some  other  part  of  the  human  body  as  the  arm  or  a  finger, 
was  utilized  in  measurement  reuse.  In  later  and  better  systems 
units  such  as  the  meter  have  been  devised.  These  units  are  more 
uniform  than  the  former  anatomical  ones,  and  are  better  adapted  in 
many  other  ways  to  meet  fundamental  and  far-reaching  conditions 
of  Hfe.  Similarly  the  atom  has  been  devised  to  give  a  certain  kind 
of  control  of  the  material  universe,  and  electrical  units  to  perfect 
the  use  of  electricity.  In  a  word,  in  the  processes  of  reuse,  the 
unit  creates  the  multiplier  and  result.  On  the  other  hand,  in  the 
unit  and  multiplier,  the  multiplier  and  result  may  create  the  unit. 

Other  advantages  in  the  use  of  the  unit  and  multiplier  will  be 
evident  after  we  have  catalogued  and  illustrated  the  different  princi- 
pal forms  which  these  instruments  of  efficiency  may  assume. 

CXASSIFI CATION  OF  UNITS 

Units  Classified  According  to  their  Materials 

Units,  like  the  data  of  reuse,  may  be  classified  either  according  to 
the  character  of  the  rnaterials  of  which  they  are  composed,  or  ac- 
cording to  the  forms  which  they  assume. 

With  reference  to  the  materials  composing  them,  units  are 
classified  in  much  the  same  way  as  are  the  data  of  reuse  (see  pp. 
15-18).  Thus  we  may  have  an  irwrganic  unit  such  as  an  atom, 
molecule,  or  crystal,  or  any  object  composed  of  these.  Similarly 
we  may  have  as  a  unit  of  work  the  horse-power,  or  the  energy  re- 
quired to  lift  33,000  pounds  one  foot  in  one  minute.  So  also  we 
may  have  biologic  units  of  various  kinds,  as  cells,  tissues,  organs,  or 
entire  organisms  such  as  different  plants  or  animals.  Similarly  we 
have  psychic  units,  examples  being  perceptions,  feelings,  ideas,  or 
acts.  Social  and  political  units  are  also  in  use,  as  cities,  counties, 
and  states.  So  each  department  of  thought  and  action  contains  its 
own  characteristic  units.  Various  examples  of  these  departmental 
units  will  be  given  in  the  course  of  the  discussions  which  follow. 

It  may  be  well  to  state  at  this  place  that,  owing  to  the  more 
abstract  nature  of  units,  many  of  the  limitations  mentioned  on 
p.  18  with  respect  to  materials  proposed  for  reuse  do  not  apply 
to  the  same  extent  to  objects  treated  as  units  in  a  multiplicative 
process. 


UNIT  AND   MULTIPLIER  37 

Units  Classified  According  to  Form 

We  next  consider  the  classification  of  units  according  to  their 
forms  or  certain  other  abstract  characteristics. 

Considered  with  reference  to  the  categories  of  space  and  quantity, 
units  may  be  grouped  according  to  their  size,  shape,  or  position. 

With  respect  to  number,  units  may  be  single,  dual,  triadic,  or 
n-fold,  according  to  the  number  of  elements  composing  them.  Thus 
the  ton-mile  and  acre-foot  are  each  dual  in  nature.  The  unit  of 
work  mentioned  above  (the  horse-power)  is  triadic.  The  numerical 
characteristic  of  units  is  frequently  expressed  as  the  number  of 
dimensions  in  the  unit. 

As  to  time  units  may  be  temporary  or  lasting. 

As  to  force  they  may  be  active  or  passive. 

Natural  and  Artificial  Units 

Since  more  or  less  artificial  units  are  the  source  of  special  superior 
results  which  are  characteristic  of  the  unit  and  multiplier  principle, 
the  distinction  between  natural  and  artificial  units  is  of  the  first 
importance  for  our  purpose. 

A  natural  unit  is  any  individual  object  as  we  find  it  in  the  world 
about  us,  as  a  man,  tree,  grain  of  wheat,  or  a  day. 

A  semi-artificial  unit  is  a  natural  object  which  has  been  partially 
modified  so  as  to  facilitate  its  use  as  a  unit.  An  example  is  the 
mean  or  average  of  a  number  of  objects,  as  the  mean  solar  day, 
or  the  fractional  part  of  a  physically  undivided  object,  as  ^  of  the 
area  of  the  United  States.  Another  instance  is  a  room  in  a  house 
taken  as  a  measure  of  the  size  of  the  house,  as  when  we  speak  of  a 
six-room,  or  an  eight-room  house.  A  like  case  is  the  description  of 
a  cotton  farm  in  the  Soifth  as  a  one-mule  or  a  two-mule  farm. 

The  value  of  slightly  artificial  units  is  illustrated  by  the  operation 
of  that  form  of  universal  suffrage  where  one  man  has  one  vote, 
regardless  of  differences  among  men,  and  questions  are  decided  by 
the  principle  of  majorities.  Among  the  advantages  which  arise 
from  this  somewhat  artificial  idea  of  uniformity  among  voters  are 
the  ease  and  speed  with  which  decisions  are  thus  obtained  as  com- 
pared with  decisions  left  to  popular  plaudits,  riots,  or  revolutions, 
and  often  to  a  series  of  violent  actions  and  reactions.  It  is  to  be 
noted  that  in  this  use  of  the  average  voter,  the  inequalities  among 
men  are  not  wholly  ignored  but  are  left  to  adjust  themselves  by 


38  SOURCES  OF  EFFICIENCY 

indirect  methods  as  by  the  various  influences  which  more  able  men 
exert  upon  those  less  able. 

An  artificial  unit  is  a  unit  devised  by  man.  Instances  of  such 
units  are  an  hour,  dollar,  or  pound ;  a  lesson,  dose,  or  experiment,  a 
letter,  word,  sentence,  paragraph,  page.  Other  more  extreme  illus- 
trations are  the  various  legal  fictions,  such  as  the  one  which  regards 
a  corporation  as  a  person,  or  the  hypothetic  units  employed  in 
science  and  in  philosophy. 

A  set  of  units  often  forms  a  series  increasing  regularly  in  size 
or  in  importance  in  some  other  way.  The  inch,  foot,  yard,  and  mile 
form  an  example  of  such  a  scale  of  units.  Similar  instances  are 
furnished  by  the  different  tables  of  compound  numbers  given  in 
Arithmetic.  Each  developed  field  of  work  is  usually  supplied  with 
such  a  set  of  units  in  some  shape.  Such  scales  of  units  will  be 
treated  more  fully  in  Chapter  VI  (p.  95). 

Many  other  special  forms  of  units,  each  of  more  or  less  value,  will 
appear  as  we  proceed. 

It  is  also  to  be  observed  that  units  of  the  various  kinds  mentioned 
above  may  be  combined  to  form  a  vast  variety  of  complex  units.  An 
instance  of  a  complex  unit  is  a  library,  or  a  civilization. 

CLASSIFICATION   OF   MULTIPLIERS 

A  multiplier  is  primarily  a  number  but  this  numerical  essence  in 
many  cases  is  embodied  in  certain  materials  or  entities,  which, 
while  disguising  the  nature  of  the  multipliers  in  some  ways,  in 
others  furnish  the  immediate  instrumentalism  by  which  the  multi- 
plier is  handled  or  applied  (see  pp.  49-50  for  analysis  and  definition 
of  multiplier). 

Classification  of  Multipliers  According  to  Materials 

It  is  convenient  to  classify  many  multipliers  according  to  the 
materials  in  which  they  are  thus  more  or  less  embodied. 

Many  kinds  of  what  may  be  regarded  as  material  or  concrete 
multipliers  are  in  use.  For  instance,  from  one  point  of  view,  the 
lever  is  a  multiplier  of  man's  available  energy.  In  like  manner 
every  mechanical  appliance  which  is  a  modification  of  the  lever,  as 
the  wheel,  pulley,  inclined  plane,  screw,  and  every  machine  composed 
of  these,  is  a  multiplier  belonging  to  the  same  general  class. 

Many  other  instruments  used  by  man  are  multiplicative  agencies. 
Thus  the  lens  manifolds  man's  power  to  see  both  small  objects  and 


UNIT  AND   MULTIPLIER 


39 


distant  objects.  In  the  same  class  of  multipliers  may  be  mentioned 
the  sounding  board  of  a  piano,  the  needle  and  mirror  of  a^^alvano- 
meter,  the  relay  circuit  of  a  telegraph  instrument,  and  the  vibrating 
membrane  of  a  telephone  receiver.  In  fact,  from  one  point  of 
view,  all  the  machinery  which  man  uses,  taken  as  a  whole,  may  be 
regarded  as  a  gigantic  multiplier  of  his  power. 

An  instance  of  a  different  kind  of  material  multiplier  is  the  use 
of  capital  to  enlarge  the  application  of  the  business  power  in  a  man. 

Similarly  various  forces  in  nature,  when  properly  applied,  become 
in  effect  multipliers  of  man's  power  to  achieve  results.  The  hole 
drilled  in  a  rock  (the  unit)  is  vastly  increased  by  the  explosion  of  a 
charge  of  dynamite  (the  multiplier).  In  a  much  larger  sense,  coal 
and  water-power  are  mani folders  of  man's  power.  Acting  in  con- 
junction with  mechanical  multipliers  these  forces  produce  note- 
worthy results.  Thus  it  is  estimated  that  the  steam  and  gas  engines 
in  use  in  the  world  do  the  physical  work  of  2,000,000,000  of  men 
and  thus  increase  the  manual  power  of  the  human  race  at  least 
sevenfold. 

It  is  to  be  noted  in  this  connection  that  motion  from  certain  points 
of  view  may  be  regarded  as  a  multiplier.  Thus  it  is  possible  for  a 
man  of  small  resources  to  manifold  them  by  keeping  them  in  rapid 
action.  Also  we  have  the  case  of  a  point  generating  a  line  by 
motion,  and  similar  geometric  illustrations.  The  physical  and  chemi- 
cal properties  of  matter  under  certain  circumstances  are  important 
multipliers  of  man's  powers.  Thus  a  granite  monument,  or  the 
chemical  and  physical  properties  of  granite  which  make  such  a 
monument  lasting,  multiply  an  inscription  carved  on  the  monument 
by  means  of  the  duration  imparted  to  the  inscription.  So  ink  and 
paper  impart  a  certain  permanence  to  a  fact  or  idea  recorded  by 
their  use  and  give  a  manifold  extension  to  such  records. 

The  biological  field  is  full  of  illustrations  of  the  principle  in  hand. 
The  oolites  and  certain  bones  in  the  ear  are  magnifiers  of  the  vibra- 
tions in  the  membrane  of  the  ear  made  by  sound  waves.  Other 
nerves  of  sensation  have  multipliers  of  different  kinds,  as  hairs, 
papillae,  etc.  Many  of  the  bones  of  the  body  act  as  levers  in  other 
ways.    Reproduction  itself  is  a  process  of  multiplication. 

More  Abstract  Multipliers 

In  the  realm  of  mind,  psychic  units  have  different  multipliers  as 
memory,  imagination,  reason,  fear,  surprise,  joy,  interest,  faith,  and 


40 


SOURCES  OF  EFFICIENCY 


courage.  In  connection  with  an  act  of  wrong  doing,  deliberate  in- 
tention accompanying  an  act  gives  it  a  peculiar  gravity.  So  in 
ethics,  the  spirit  in  which  a  gift  or  sacrifice  is  made  is  a  multiplier 
of  its  value. 

Special  mention  should  be  made  of  certain  imperfectly  under- 
stood subjective  multipliers,  such  as  that  psychic  action  which 
enlarges  perceptions  of  discrete  phenomena  into  a  continuity;  or 
that  complex  of  different  multiplicative  powers  which  expands  a 
hint  or  suggestion  into  a  complete  whole;  or  causes  that  which  is 
partly  hidden  to  be  most  fully  expressed. 

Many  social  agencies  are  multipliers  of  a  high  order  of  power. 
Among  these  are  language,  the  printing  press,  railroads,  the  post- 
office,  publicity,  political  systems,  and  civilization  as  a  whole. 

In  a  certain  sense  the  quality  of  a  unit  is  its  multiplier.  Thus  the 
power  of  an  act  is  multiplied  if  this  act  be  applied  to  the  apexal  (or 
strategic)  point  in  a  domain  of  material.  Thus  the  dog  jumps  for 
the  throat  of  its  victim ;  and  the  bee  when  attacking  a  person  tries 
to  sting  the  eye.  Hence  comes  the  importance  of  acting  at  a 
psychological  moment,  or  of  seizing  a  strategic  point,  or  of  con- 
trolling routes  of  transportation  in  business  and  in  war.  Hence 
also  the  value  of  being  able  to  influence  processes  of  education,  and 
of  being  able  to  control  the  fountain  sources  or  underlying  causes 
of  any  movement.  Reform  a  man,  it  has  been  said,  and  you  reform 
one  man ;  reform  a  boy  and  you  reform  a  whole  multiplication  table 
of  men. 

Multipliers  Classified  by  Forms 

Multipliers  may  also  be  characterized  and  classified  according  to 
certain  formal  elements  prominent  in  them.  Since  material  often 
in  a  measure  determines  form,  in  many  of  the  species  to  be  men- 
tioned in  this  relation  form  and  material  are  closely  connected. 

A  multiplier,  like  a  unit,  may  be  characterized  numerically.  For 
instance,  when  we  kill  two  birds  with  one  stone,  the  multiplier  is 
dual  in  power  and  effect.  In  like  manner  it  is  evident  that  it  may  be 
any  other  number  large  or  small.  Also  a  multiplier  may  be  dual  (or 
larger)  numerically  in  that  it  is  a  combination  of  two  (or  more) 
multiplicative  agencies.  Thus  a  dual  multiplier  may  be  formed 
by  the  combination  of  a  subjective  and  objective  multiplier,  as 
when  conscience  and  public  opinion  unite  in  the  condemnation  of  a 
given  act. 


UNIT  AND   MULTIPLIER  41 

A  multiplier  may  also  be  characterized  by  some  spatial  principle 
prominent  in  it.  For  instance  a  multiplier  may  be  linear  m  form. 
Thus  when  a  cannon  ball  is  fired  not  across  but  down  a  line  of 
soldiers  its  effect  is  multiplied  in  a  linear  way.  Similarly  we  have 
mani folders  that  are  fan-shaped,  conically  expanding,  radiating  from 
the  center  of  a  circle  or  sphere,  spreading  like  the  trunk  and 
branches  of  a  tree,  or  of  other  geometric  forms.  Similarly  a  multi- 
plier may  be  one,  two,  three,  or  w-dimensional  in  character. 

An  important  spatial  case,  though  one  often  difficult  to  analyze 
completely,  is  that  where  the  multiplying  power  is  due  to  relative 
position.  Thus  in  the  number  876508  the  left  hand  8,  as  compared 
with  the  right  hand  8,  is  multiplied  one  hundred  thousand  times  in 
value  by  its  relative  position.  Similarly  position  is  a  multiplier  of 
one's  power  in  many  social  and  other  relations. 

A  margin  of  empty  space  also,  by  virtue  of  its  power  to  give 
freedom  and  room  for  expansion,  often  constitutes  an  important, 
though  sometimes  subtle  enlarger  of  utilities. 

With  respect  to  time  a  multiplier  may  be  temporary  or  permanent. 
Often  also  time  itself  is  spoken  of  as  a  multiplier  though  time  in  this 
case  is  of  course  but  a  symbol  for  the  causes  or  multipliers  acting 
in  time.  With  respect  to  time  we  also  have  predictive  multiplication 
as  when  a  gardener  multiplies  the  efficiency  of  his  work  by  killing 
young  weeds  before  they  have  broken  the  surface  of  the  ground. 
In  fact  many  of  our  mental  powers  such  as  fear,  conscience,  inter- 
est, or  even  reason,  have  predictive  multiplication  as  one  of  their 
chief  functions. 

By  reciprocal  multiplication  is  meant  the  action  of  two  objects 
each  of  which  acts  as  both  unit  and  multiplier  with  respect  to  the 
other.  Illustrations  are  the  hunter  and  his  dog,  the  general  and  his 
army,  theory  and  practice,  matter  and  form,  labor  and  capital,  the 
plan  and  elevation  of  a  building,  humor  and  pathos,  two  friends, 
two  elements  in  a  good  dish,  as  pork  and  beans,  two  flowers  which 
fertilize  each  other.  Also  any  number  of  elements  may  enter  into 
a  reciprocal  multiplicative  relation.  Thus  when  a  number  of  friends 
or  business  men  cooperate,  the  ideas  of  one  member  of  the  circle  are 
multiplied  (often  many  times)  by  the  use  made  of  them  by  other 
members  of  the  circle. 

Multipliers  may  be  of  different  orders  of  power.  This  matter  also 
will  be  discussed  more  fully  later  (pp.  51-52). 


42  SOURCES  OF  EFFICIENCY 

Indirect  and  Obscure  Multipliers 

Some  multipliers  are  negative  in  character.  An  instance  is  the 
removal  of  an  obstacle  in  order  that  a  direct  multiplier  may  act. 
Thus,  instead  of  fanning  oneself  on  a  hot  day,  one  may  often  get  the 
same  result  with  far  less  labor  by  opening  a  window  and  letting  a 
breeze  blow  through  the  room.  In  a  vastly  higher  field  results  of 
the  first  importance  are  often  achieved  by  merely  setting  free  intel- 
lectual or  social  forces.  Most  important  for  our  purpose  is  the 
disentanglement  of  the  prime  efficiency  agents  or  principles  in  a 
given  domain  and  allowing  them  to  act  without  hindrance. 

Another  important  kind  of  negative  multiplication  is  that  of 
division  of  error  or  loss.  Thus  if  we  assay  a  specimen  of  the  ore 
in  a  poor  mine  before  working  the  mine  extensively,  we  may  divide 
by  thousands  t'he  loss  which  would  have  resulted  from  attempting  to 
operate  the  mine  on  a  large  scale.  In  general,  every  experiment  or 
testing  on  a  small  scale  of  a  proposed  plan  or  method,  constitutes  a 
unit  which,  if  successful,  will  later  have  a  positive  multiplier,  but 
which  if  it  fails  to  give  good  results  has  a  negative  multiplier  in  that 
it  prevents  extensive  loss. 

Multipliers  are  often  vague  or  obscure  in  whole  or  part.  In- 
stances are  that  action  in  an  organism  by  which  small  doses  of  a 
vaccine  or  serum  lead  to  immunity  from  a  specified  disease.  Other 
instances  are  various  kinds  of  influence,  growth,  and  propagation. 

Complex  Multipliers 

The  diflferent  species  of  multipliers  enumerated  above  may  be 
compounded  and  complexed  together  in  various  ways.  Thus,  to 
consider  an  extreme  case,  various  objective  multipliers  compounded 
together  give  us  our  whole  system  of  civilization  as  a  multiplier  of 
any  good  (or  evil)  unit.  Similarly  subjective  multipliers  when  com- 
bined give  us  the  entire  mind  and  its  experiences  as  an  enlarger  of 
any  impression. 

Subjective  and  objective  multiplicative  agencies  give  us,  for 
example,  the  system  of  credit  and  banking  which  multiplies  the 
usefulness  of  the  small  stock  of  gold  possessed  by  the  world;  or 
the  process  which  has  expanded  the  observation  of  the  attractive 
power  of  a  piece  of  rubbed  amber  into  the  science  and  art  of  elec- 
tricity; or  that  which  has  enlarged  the  observation  of  the  smudge 
made  by  sunlight  on  a  piece  of  silver  into  the  science  and  art  of 
photography. 


UNIT  AND   MULTIPLIER  43 

An  important  special  case  of  the  complex  multiplier  is  that  which 
often  creates  enormously  large  rewards  for  the  winner  of  a  ra^e  by  a 
margin  however  small.  Similar  are  the  multipliers  which  act  in  the 
process  of  evolution  and  cause  those  organisms  to  prevail  and  sur- 
vive which  excel  by  however  small  a  margin  of  fitness. 

An  important  special  case  of  abstract  and  complex  multiplier  is 
the  process  called  generalization. 

For  our  purpose  the  most  comprehensive  and  powerful  multi- 
pliers will  be  found  to  be  the  principles  of  efficiency  which  are  being 
investigated  in  this  book. 

ADVANTAGES  IN  THE  USE  OF  UNITS  AND  MULTIPLIERS 

Many  of  the  statements  that  were  made  in  Chapter  II  (pp.  23-26) 
concerning  the  efficiency  functions  of  reuse  apply  also  to  the  unit  and 
multiplier.  But  the  fact  that  the  unit  and  multiplier  principle  is  more 
abstract  and  general  (less  restricted  as  to  the  categories  of  person- 
ality and  time)  gives  it  in  some  respects  a  deeper  and  broader  mean- 
ing and  usefulness.  Just  as  the  unit  and  multiplier  process  is  more 
thoroughgoing  and  manageable  so  also  are  its  fruits. 

Other  Superiorities  to  Reuse 

For  instance,  the  application  of  a  pulley  to  lift  a  weight  may  be 
viewed  either  as  a  case  of  reuse  or  as  a  case  of  the  multiplication  of 
one's  powers.  The  advantage  of  expressing  the  process  in  the 
unit  and  multiplier  form  is  that  it  enables  us  to  adapt  our  pulley 
machinery  accurately  to  the  size  of  the  weight  to  be  lifted,  and  thus 
at  times  to  avoid  costly  experiments  and  much  waste  of  energy. 
Similarly  in  many  other  cases  by  putting  a  given  efficiency  principle 
in  the  unit  and  multiplier  form,  we  obtain  increased  economy  or 
efficiency  in  its  application. 

The  superior  efficiency  of  highly  developed  forms  of  the  unit  and 
multiplier  principle  over  more  or  less  haphazard  reuse  is  illustrated 
by  a  comparison  of  the  English  language  with  the  Chinese.  The 
printing  of  English  has  been  reduced  to  the  use  of  a  few  well 
selected  units  with  large  multipliers,  while  the  Chinese  characters 
still  consist  of  a  multitude  of  ancient  ideographs.  As  a  result  a 
font  of  English  type  weighs  50  pounds  and  costs  $5  while  a  font  of 
Chinese  type  weighs  1000  pounds  and  costs  $100.  Furthermore 
the  typewriter  and  linotype  greatly  facilitate  the  use  of  the  English 
language,  but  cannot  be  employed  in  the  use  of  Chinese  because  of 


44  SOURCES  OF  EFFICIENCY 

the  multitude  of  its  primary  symbols.  The  comparative  inefficiency 
of  the  Chinese  language  is  also  illustrated  by  the  fact  mentioned  on 
a  previous  page  that  the  Chinese  compositor  walks  20  miles  a  day 
while  the  compositor  of  English  type  stands  still. 

Increase  of  Power  obtained  by  Multiplication  of  Units 

Machines  also,  by  the  reuse  of  which  they  are  capable,  increase 
human  power.  But  this  increase  is  greatly  magnified  by  standard- 
izing machines,  that  is,  by  reducing  machines  as  far  as  possible  to 
the  unit  and  multiplier  form. 

Similarly  the  reciprocal  reuse  of  their  work  by  scientific  men  is 
much  enlarged  by  putting  the  results  of  their  work  in  a  manifold 
unit  and  multiplier  form  as  in  journals  and  periodicals,  and  by  ex- 
pressing these  results  as  far  as  possible  as  principles,  laws,  and 
formulas  stated  in  terms  of  more  or  less  conventional  units. 

Systems  due  to  Units  and  their  Multipliers 

This  suggests  a  still  more  general  and  far-reaching  advantage 
which  characterizes  the  use  of  the  unit  and  multiplier  methods  viz. : 
the  fact  that  the  development  of  adapted  species  of  unit  and  multi- 
plier often  leads  to  the  combination  of  these  into  extended  systems 
with  a  corresponding  development  of  efficiency  results. 

Duality  of  Unit  and  Multiplier  a  Source  of  Power 

Another  specific  and  prime  source  of  efficiency  in  the  use  of  the 
unit  and  multiplier  is  found  in  the  duality  which  characterizes  the 
unit  and  multiplier  when  considered  in  comparison  with  the  single 
concept  prominent  in  the  principle  of  reuse.  As  a  result  each  of  the 
two  instruments  involved,  the  unit  and  the  multiplier,  can  be  devel- 
oped in  independent  aggressive  fashion.  Thus  the  unit  can  be 
adapted  to  any  given  purpose  and  the  multiplier,  owing  to  its 
expHcit  numerical  form  and  abstract  nature,  can  in  like  manner  be 
freely  extended.  Also  the  limitations  of  the  dual  concepts  may  be 
more  readily  studied  and  remedied,  and  auxiliary  objects,  such  as 
symbolisms,  may  be  more  readily  applied  to  them. 

Transcendent  Results 

The  result  of  a  multiplication  often  transcends  in  some  special 
way  the  data  employed.    Thus  a  drop  of  water  when  multiplied  be- 


UNIT  AND   MULTIPLIER  45 

comes  the  ocean.  But  the  ocean  is  much  more  than  a  drop  of  water 
with  a  numerical  muhiplier.  So  rock  is  more  than  a  grain  of  sand 
or  an  atom  manifolded. 

Taking  up  a  different  form  of  transcendence,  the  microphone  by 
multiplying  the  force  of  a  vibration  makes  the  vibration  audible  and 
the  microscope  by  multiplying  the  light  which  falls  on  the  retina 
of  the  eye  causes  the  invisible  to  be  seen.  A  disease  germ  when 
multiplied  may  produce  first  sickness  and  then  death.  A  variation 
in  the  anatomy  of  a  reptile  when  given  a  large  multiplier  has  pro- 
duced the  bird.  A  point  when  multiplied  by  motion  produces  a 
line.  Trifles  when  multiplied  together  in  a  work  of  art  beget  what 
is  called  perfection.  According  to  the  law  of  evolution  a  multiplica^ 
tive  increase  in  the  number  of  individuals  belonging  to  a  species, 
leads  on  the  one  hand  to  the  death  of  many  individuals  in  the  species, 
and  on  the  other  hand  to  the  development  of  other  individuals  into 
a  higher  kind  of  organism.  In  many  different  domains  a  multiplica- 
tive accumulation  of  minute  changes  often  produces  a  conversion  or 
a  revolution.  These  transformational  fruits  may  all  be  hastened  and 
increased  by  the  choice  or  creation  of  adapted  units  and  multipliers, 
as  contrasted  with  more  accidental  reuse. 

Progress  obtained  in  Various  Departments 

We  may  realize  the  importance  of  the  unit  and  multiplier  princi- 
ple in  a  more  pictorial  way  by  noting  that  the  history  of  human 
progress,  in  one  aspect,  has  been  largely  a  history  of  improving 
units  and  multipliers.  Thus  in  the  field  of  inorganic  science,  pro- 
gress has  been  made  by  the  use  of  the  atoms  devised  by  the  ancient 
world,  and  still  further  progress  by  replacing  atoms  in  part  by  ions 
and  electrons.  So  immense  advances  have  been  made  in  biology  by 
recognizing  the  cell  as  the  fundamental  unit,  and  in  political  life  by 
regarding  the  individual  citizen,  not  the  tribe  or  the  city,  as  the 
primal  unit.  The  same  source  of  increasing  efficiency  is  prominent 
in  other  departments  of  life  or  thought. 

Historical  Illustrations  of  Advantages 

In  like  manner  human  progress  has  been  marked  by  increasing  and 
improving  multipliers,  and  every  period  of  unusual  achievement  has 
been  one  where  large  intense  multipliers  have  been  at  work.  Thus 
the  epochs  of  Greek  and  Italian  art,  the  cathedral  building  age,  the 


46  SOURCES  OF  EFFICIENCY 

various  religious  eras,  each  came  and  flourished  when  they  did, 
from  one  point  of  view,  because  of  the  large  popular  multipliers  of 
the  new  item  of  efficiency  or  value  connected  with  each  of  these 
periods.  More  recently  the  printing  press,  the  railroad,  steamboat, 
telegraph,  and  similar  agencies  have  produced  new  multipliers 
which  have  given  new  values  to  every  unit  of  progress  and  greatly 
accelerated  many  forward  movements. 

Also  in  the  history  of  progress  new  units  and  new  multipliers 
have  acted  and  reacted  on  each  other  in  various  ways.  This  is 
illustrated  by  the  fact  that  the  new  social  and  political  units  in  the 
United  States  have  given  rise  to  vast  multipliers  of  every  new  in- 
vention and  improvement.  The  new  multipliers  in  turn  have  led  to 
the  development  of  new  units,  particularly  of  small  units  which 
could  not  have  established  themselves  but  for  the  large  multipliers 
ready  to  be  applied  to  them.  These  new  units  are  illustrated  in 
the  numerous  small  improvements  made  in  various  machines  and 
tools. 

Advantages  Illustrated  by  Great  Men 

Similarly  every  great  man  as  a  part  of  his  work  has  created  at 
least  one  new  efficiency  unit,  or  given  some  old  unit  a  new  and  nota- 
ble multiplier.  Thus  Christ  brought  into  the  world  in  a  vitally  new 
form  the  principles  of  the  fatherhood  of  God  and  the  brotherhood 
of  man.  Paul  by  his  knowledge  of  the  Greek  philosophy  and  the 
Roman  political  system  gave  a  large  multiplier  to  the  units  which 
Christ  supplied. 

Departments  Determined  by  Units  and  Multipliers 

In  a  fuller  sense  also  we  see  that  every  department  of  knowledge 
or  activity  is  based  on  (or  means)  a  few  fundamental  units  reused 
and  multiplied.  This  principle  holds  true  even  in  apparently  in- 
formal and  unsystematic  fields  of  activity.  Thus  we  have  the  ele- 
mentary units  of  dancing,  a  few  fundamental  strokes  in  penmanship, 
and  similar  primary  units  in  boxing  and  music.  Likewise,  though 
often  in  a  far  higher  sense,  each  branch  of  science  has  its  alphabet, 
grammar,  and  logic,  and  because  of  the  great  and  distinct  body  of 
economy  and  efficiency  thus  generated  its  existence  as  a  distinct  de- 
partment is  justified. 


UNIT  AND   MULTIPLIER  47 

Absence  of  Units  and  Multipliers  Means  Loss 

Another  collective  way  in  which  to  realize  the  value  and  impor- 
tance of  the  unit  and  multiplier  principle  is  to  try  to  picture  what 
life  would  be  without  this  instrument  of  efficiency.  In  this  case 
mankind  would  need  to  dispense  with  the  dollar,  mile,  inch,  quart, 
day,  year;  with  the  science  of  number  and  measurement;  and  with 
the  more  informal  sets  and  systems  of  units  and  multipliers  which 
pervade  all  life. 

Limitations  in  the  Utility  of  Units  and  Multipliers 

Before  closing  this  presentation  of  the  efficiency  functions  of  the 
unit  and  multiplier,  some  statement  should  be  made  of  the  limita- 
tions connected  with  this  source  of  efficiency.  Prominent  among 
these  are  certain  limitations  in  the  nature  of  things  (to  be  studied 
more  fully  later,  see  p.  265)  which  on  the  one  hand  often  prevent 
the  formation  of  units  and  on  the  other  check  the  action  of 
multipliers. 

Also  a  unit  may  be  evil  or  destructive  in  its  nature;  hence  its 
multiplier  may  operate  to  produce  injurious  results.  Illustrations 
are  the  Colorado  potato  beetle,  the  gypsy  moth,  and  mistakes  and 
sins  of  all  kinds. 

Also  the  unit  and  multiplier  principle  has  certain  drawbacks  due 
to  the  abstract  and  impersonal  nature  of  units  and  of  number. 
Hence  arises  the  need  of  other  efficiency  principles  to  be  used  in 
connection  with  the  one  under  consideration. 

Complex  Fruits 

It  is  evident  that  the  various  fruitages  of  the  unit  and  multiplier 
may  be  compounded  and  complexed  in  many  ways.  In  this  connec- 
tion the  operation  of  the  principle  of  dialectic  (see  Chapter  XIV,  p. 
249)  is  important.  Thus  a  single  observation  made  by  Prof.  Roent- 
gen has  developed  into  the  whole  science  of  X-rays  with  its  world 
of  surgical  and  other  more  general  applications. 

The  most  important  use  of  the  unit  and  multiplier  principle,  as 
will  later  be  made  more  evident,  is  the  power  of  this  agent  to  set 
free  and  develop  other  efficiency  principles  both  objectively  and 
subjectively. 


48  SOURCES  OF  EFFICIENCY 

ANALYSIS   OF  THE  UNIT   AND    MULTIPLIER 

A  general  statement  of  the  improved  sources  of  efficiency  in  the 
unit  and  multiplier  principle  was  made  on  pp.  35-36.  In  making 
a  closer  examination  of  this  matter  it  will  be  an  advantage  to  make 
use  of  the  principle  of  marginal  reuse  as  presented  in  Chapter  II 
(p.  19).  Thus  by  showing  in  what  respects  the  unit  and  multipHer 
principle  differs  from  reuse,  we  utilize  the  work  which  has  already 
been  done  in  analyzing  and  defining  reuse. 

Tabular  Comparison 

The  corresponding  qualities  and  elements  which  enter  into  the 
two  principles  under  discussion  are  shown  in  the  following  table : 

Reuse  Unit  and  Multiplier 

Personal  Impersonal 

Time  is  essential  Time  is  secondary  and  quantity  is 

primary 

Emphasis  on  datum  and  result     Emphasis  on  process 

Concrete  Abstract 

Fruitage  usually  direct  and  im-  Fruitage  often  indirect  and  re- 
mediate mote 

Qualitative  Quantitative 

Voluntary  and  intentional  Multipliers   often   act  independ- 

ently of  or  even  contrary  to 
human  will 

Synthetic  Analytic 

Summing  up  the  matter  in  a  single  sentence,  reuse  is  concrete,  in- 
dividual, subjective,  empirical,  opportunistic,  geometric,  often  ir- 
regular and  haphazard ;  the  unit  and  multiplier  principle  is  abstract, 
social,  objective,  systematic,  analytical,  logical,  artificial,  algebraic. 

We  may  also  proceed  in  our  analysis  of  the  principles  in  hand 
by  anticipating  to  some  extent  certain  principles  of  efficiency  to  be 
treated  later  and  by  showing  the  relation  of  the  unit  and  multiplier 
principle  to  certain  other  primal  sources  of  efficiency. 

Relation  to  Other  Efficients 

Thus  with  respect  to  the  diversity  or  separation  principle  (see 
Chapter  VIII)  the  unit  and  multiplier  method  is  based  externally 
on  a  certain  freedom  from  the  entanglements  of  space,  time,  and 
personality,  and  internally  consists  essentially  in  a  specific  distinc- 
tion between  the  unit  and  the  multiplier.     The  treatment  given 


UNIT  AND  MULTIPLIER  49 

later  of  diversity  as  a  source  of  efficiency  will  show  how  each  of 
these  separations  opens  the  way  to  a  group  of  advantages,  ^me 
abstract,  and  some  concrete. 

Similarly  with  respect  to  the  principle  of  uniformity  the  unit  and 
multiplier  data  and  processes  may  often  be  standardized  and  thereby 
largely  increased  in  power.  With  respect  to  orders  of  material 
(see  Chapter  VI)  the  unit  and  multiplier  agency  is  as  a  rule  of 
higher  order  than  reuse.  With  respect  to  the  categories  of  mo- 
tion and  force,  it  is  more  active  and  rapid.  It  also  has  a  larger 
dialectic  power.  With  respect  to  directive  use  it  is  more 
manageable. 

It  should  also  be  noted  that  the  principle  of  limitation  acts  in 
important  ways  in  the  formation  of  the  reuse  and  unit  and  multi- 
plier agencies.  For  instance  there  would  be  no  need  for  the  em- 
ployment of  either  of  these  principles  of  efficiency  if  certain  limita- 
tions did  not  exist  and  compel  the  use  of  such  methods.  Hence 
the  study  of  the  meaning  and  forms  of  limitation  should  aid  us  in 
the  development  and  application  of  each  of  the  two  principles 
under  discussion. 

Analysis  of  Special  Case 

A  word  should  also  be  said  about  the  nature  and  classification 
of  certain  special  cases  of  efficiency  which  are  at  least  closely  con- 
nected with  the  idea  of  the  unit  and  multiplier.  For  instance  if 
we  bait  a  hook  with  a  piece  of  meat  and  catch  a  fish,  the  question 
may  be  raised  as  to  whether  the  bait  may  be  regarded  as  a  unit 
and  the  fish  caught  as  the  product.  A  similar  question  may  be 
asked  as  to  a  seed  which  is  planted  and  the  yield  which  results.  In 
the  one  case  the  bait  is  lost  as  food.  In  the  other  the  seed  is  partly 
lost  and  partly  transformed  into  the  resulting  crop;  certain  elements 
of  soil  and  atmosphere  also  enter  into  the  matter.  Hence  we  may 
say  that  in  the  direct  aspect  the  question  is  a  complicated  one,  but 
that  if  we  reduce  the  matter  in  each  case  to  an  amount  of  energy 
expended,  and  a  return  of  energy,  we  find  that  both  cases  are  es- 
sentially instances  of  unit  and  multiplier.  The  same  analysis  applies 
to  a  variety  of  like  cases. 

Definitions 

Before  closing  this  part  of  the  discussion  it  may  be  well  to  formu- 
late, as  best  we  can,  definitions  of  the  unit  and  multiplier. 


50  SOURCES  OF  EFFICIENCY 

A  unit  is  any  entity  used  manifoldly  in  space  or  time  or  in  any 
relation. 

The  multiplier  expresses  the  number  of  manifold  uses  made  of 
a  unit. 

The  various  elements  which  our  analysis  has  made  clear  as  en- 
tering into  the  unit  and  multiplier  principle  may  all  be  made  the 
means  of  a  more  effective  application  of  the  principle.  Some  of  the 
improved  methods  thus  suggested  we  now  proceed  to  point  out. 

METHODS  OF  APPLICATION 

Repetition  of  Advantages  in  Reuse 

Many  of  the  remarks  made  in  Chapter  II  in  connection  with  the 
best  methods  of  utilizing  the  principle  of  reuse  apply  also  to  the 
unit  and  multiplier.  However  the  fact  that  the  unit  and  multiplier 
concept  is  more  abstract  and  general  than  reuse  gives  rise  to  im- 
portant additional  considerations. 

Adaptation  of  Unit  and  Multiplier  to  Each  Situation 

Owing  to  the  fact  that  both  unit  and  multiplier  may  take  many 
diverse  forms,  also  that  these  forms  are  adaptable  and  largely  un- 
der control,  it  is  important  to  study  each  special  case  where  a  unit 
and  multiplier  are  to  be  employed  and  to  select  the  most  efficient 
species  of  each  for  the  work  in  hand. 

As  an  aid  for  this  adaptive  work  it  is  important  to  realize  and 
keep  in  mind  in  some  systematic  way  the  large  number  of  possible 
forms  of  units,  including  particularly  the  various  forms  of  natural, 
artificial,  and  semi-artificial  units;  and  to  treat  multipliers  in  like 
manner. 

Frequent  Value  of  even  Imperfect  Units 

Where  effective  units  are  difficult  to  obtain,  it  is  important  to 
realize  the  value  of  even  imperfect  ones  in  connection  with  more 
or  less  efficient  multipliers.  Thus,  in  a  situation  of  great  difficulty, 
rather  than  do  nothing  it  is  often  well  to  make  a  start  or  beginning, 
however  crude,  and  to  trust  that  if  no  others  are  at  hand,  natural 
multipliers  will  act  on  the  unit  thus  made,  that  the  crude  initial 
units  will  improve,  and  that  new  units  and  multipliers  will  appear. 

This  procedure  of  ten.  takes  a  complex  form.  For  instance  when 
plunged  into  a  complex  and  difficult  situation  where  comprehensive 
systematic  methods  of  action  are  impossible,  it  is  well  to  give  each 


UNIT  AND  MULTIPLIER  51 

available  scrap  of  efficiency  its  largest  possible  multiplier,  and  to 
trust  that  later  developments  and  coordinations  will  appear. 

In  particular  in  cases  of  difficulty  it  is  important  to  realize  the 
value  of  such  somewhat  crude  multipliers  as  patience  and  persistence. 

Sometimes  special  methods  must  be  employed  to  get  any  unit 
whatever.  Thus  in  breeding  new  kinds  of  plants,  often  the  great 
difficulty  is  that  of  getting  a  plant  to  vary  at  all.  After  a  variation 
of  any  kind  has  been  obtained,  means  exist  of  developing  it  in 
a  desired  channel  and  often  to  high  degree.  In  other  cases  the 
difficulty  consists  in  getting  any  practical  multiplier  whatever.  Thus 
a  man  with  a  new  and  useful  idea  or  invention  may  for  a  long 
time  find  it  impossible  to  obtain  the  means  of  making  a  wide  use 
of  his  conception. 

It  is  well  to  fix  in  mind  the  rule  that  the  principle  of  the  unit  and 
multiplier  is  an  important  aid  in  all  cases  where  it  is  important  to 
make  a  little  go  a  long  way.  Thus  it  applies  to  the  problem  of 
utilizing  the  power,  without  impairing  the  scenic  grandeur,  of 
Niagara  Falls.  For  if  the  full  volume  of  water  were  sent  over  the 
Falls  during  a  specified  hour  during  each  day  and  sightseers  should 
collect  to  see  it  at  that  time,  all  the  energy  of  the  Falls  might  be 
utilized  in  a  mechanical  way  during  the  other  twenty-three  hours 
of  the  day. 

Art  of  Adapting  Units 

Methods  of  devising  units  to  meet  the  conditions  in  a  given  field 
may  be  developed  into  an  art.  Thus  instead  of  saying  that  the 
British  Empire  increased  4,000,000,000  acres  between  the  years 
1800  and  1900,  we  may  express  the  matter  much  more  effectively  for 
many  purposes  by  saying  that  the  British  Empire  during  the  nine- 
teenth century  increased  at  the  rate  of  2  acres  per  second.  So 
instead  of  saying  that  a  certain  star  is  20,000,000,000,000  of  miles 
distant,  we  may  say  that  it  is  at  a  distance  of  three  light  years.  It  is 
often  a  profitable  exercise  to  spend  one's  leisure  in  devising  units 
and  conceiving  of  their  multipliers,  and  thus  acquiring  the  art  of 
rapidly  discovering,  forming,  or  improving  these  instruments  of 
efficiency. 

A  Scale  of  Relative  Value 

As  an  important  aid  in  this  process,  it  is  desirable  to  obtain  a 
thorough  appreciation  of  the  fact  that  both  units  and  multipliers 


52  SOURCES  OF  EFFICIENCY 

may  be  of  different  orders  of  perfection  or  efficiency,  and  that  it 
is  highly  useful  to  be  able  quickly  to  recognize  and  utilize  those 
highest  in  power  under  any  given  circumstances.  For  instance  the 
most  serviceable  units  for  general  use  are  those  which  are  definite, 
permanent,  and  readily  reproducible. 

As  a  special  case  of  permanency  it  is  to  be  noted  that,  other 
things  being  equal,  old  and  established  units  are  preferable,  since 
they  have  been  frequently  tested,  already  have  large  multipliers,  and 
any  mastery  which  we  already  have  of  them  may  be  reused. 

Particular  mention  should  be  made  at  this  point  of  the  efficiency 
significance  of  the  Arabic  number  system.  When  frequently  used 
this  system  comes  to  act  almost  automatically  in  a  number  of  ways 
in  the  extension  of  results.  A  special  use  of  it  is  as  an  aid  in  the 
multiplicative  process  called  generalization.  In  generalizing  a  fact 
we  infer  that  what  is  true  of  one,  two,  or  some  objects  in  a  class, 
is  true  of  all.  In  generalizing  a  process  we  extend  the  process 
from  two  or  three  steps  to  an  unlimited  number  of  steps. 

Devising  more  Fundamental  Units 

The  power  which  we  have  of  changing  and  adapting  units  often 
enables  us  to  reduce  a  given  set  of  them  to  the  same  common  de- 
nominator, so  to  speak;  that  is,  to  more  fundamental  and  inclusive 
units.  In  certain  processes  of  mathematics,  science,  and  philos- 
ophy, this  process  has  been  carried  to  an  extreme  degree,  the 
result  being  units  of  great  abstractness  and  hence  of  inclusiveness 
and  power,  when  rightly  used.  For  the  process  of  progressive 
inclusiveness  gives  also  an  increasing  systematization  and  inter- 
relation of  units  and  other  sources  of  power. 

Best  Standard  Method 

Before  closing  this  part  oithe  discussion  it  may  be  well  to  make 
a  statement  of  the  best  standard  method  for  the  combined  use 
of  units  and  multipliers  in  the  so-called  practical  world.  As  a 
preliminary  fact  we  observe  that,  owing  to  the  highly  organized 
state  of  society,  large  multipliers  for  any  new  unit  of  advantage  are 
omnipresent,  while  only  rarely  does  a  large  new  unit  of  efficiency 
appear.  Hence  the  best  standard  method  of  employing  units  and 
multipliers  in  combination,  is  to  rely  mainly  on  small  units  and 
large  multipliers,  but  to  have  an  eye  open  for  large  units  as  ex- 


UNIT  AND  MULTIPLI.ER 


53 


ceptional  possibilities.  Thus  a  machine  which  saved  two  or  three 
drops  of  solder  in  putting  a  lid  on  a  tin  can,  produced  a  fortWe 
for  its  inventor  because  this  saving  had  a  multiplier  of  700,000,000 
each  year.  Similarly  a  fortune  was  obtained  from  the  invention 
of  the  hook  eyelet  used  on  shoes,  and  another  from  the  addition 
of  the  gimlet  point  to  the  old  fashioned  blunt  screw.  For  a  like 
reason  a  steel  manufacturer  is  ready  to  send  his  machinery  to  the 
scrap  heap  and  replace  it  by  new,  if  by  so  doing  he  can  save  10  cents 
a  ton  in  making  steel;  and  a  cotton  manufacturer  will  do  likewise 
if  he  can  save  1/16  cent  per  yard  in  making  musHn. 

In  like  manner  the  greatest  masters  of  chess  strive  primarily  not 
for  brilliant  strokes,  but  to  make  the  most  of  each  minute  advantage 
which  appears,  or  which  they  can  devise.  So  in  the  highest  forms 
of  art  the  multipliers  dominate  the  units. 

Ideal  Species  of  Unit  and  Multiplier 

It  is  well  to  remember  that,  for  general  purposes  of  thought  and 
life,  the  best  units  and  multipliers  alike,  from  our  standpoint,  are 
the  primal  efficiency  principles  which  we  are  studying  in  this  book. 
The  specific  meaning  of  this  statement  will  be  developed  later. 

Summary  of  Chapter 

At  this  point  it  will  be  well  to  recapitulate  the  substance  of  the 
present  chapter. 

The  principle  of  the  unit  and  multiplier  includes  reuse  as  a 
special  case,  and  hence  is  a  more  comprehensive  agency  of  efficiency. 
The  unit  and  its  multiplier  are  often  superior  to  reuse  in  efficiency 
because  of  the  fact  that  in  reuse  we  must  take  the  data  of  life  as 
we  find  them,  while  units  and  multipliers  may  often  be  created  and 
shaped  according  to  our  needs  and  wishes.  Innumerable  varieties  of 
both  units  and  multipliers  exist,  or  may  be  created,  each  endowed 
with  its  own  special  efficiency  powers.  Special  mention  should  be 
made  of  natural  and  artificial  units,  and  of  predictive,  reciprocal, 
and  indirect  multipHers. 

The  use  of  units  and  multipliers  means  economy  and  new 
powers  of  various  kinds.  In  some  cases  the  results  take  the  form 
of  elaborate  systems.  In  other  cases  they  are  transcendent  in  the 
sense  that  they  could  not  otherwise  have  been  obtained.  The  study 
of  great  men  and  the  history  of  human  progress  furnish  a  multitude 
of  illustrations  of  these  values. 


54  SOURCES  OF  EFFICIENCY 

In  order  to  reap  the  largest  possible  fruit  from  the  use  of  the 
units  and  their  multipliers,  it  is  necessary  to  follow  many  of  the 
methods  indicated  for  reuse  in  the  last  chapter.  Thus  it  is  im- 
portant to  realize  the  great  variety  of  possible  units  and  multipliers, 
and  to  adapt  different  forms  of  these  to  different  situations.  It  is 
an  advantage  at  times  to  arrange  units  in  a  scale  according  to  their 
relative  values,  and  to  realize  the  great  utility  of  even  an  imperfect 
unit  or  multiplier  in  a  difficult  situation.  The  ideal  species  of  units 
and  multipliers  alike  are  the  fundamental  principles  of  efficiency 
which  we  are  studying. 


EXERCISE  3 

1.  Give  an  example  of  manifold  simultaneous  use. 

2.  Also  of  use  that  is  manifold  both  in  a  simultaneous  and  a  successive 
way. 

Point  out  the  unit  and  the  multiplier  in  each  of  the  following  cases : 

3.  The  use  of  the  carpenter's  level  5.  Of  lieutenants  by  an  able  man 

4.  Of  a  parliamentary  motion  6.  Of  the  rudder  of  a  ship 

7.  The  use  of  yeast  in  making  bread. 

8.  Newton's  reputed  use  of  the  falling  apple   in  discovering  the  law  of 
gravitation. 

9.  State  which  of  the  units  employed  in  Exs.  3-8  are  natural  and  which 
artificial. 

10.  Name  some  of  the  units  employed  in  political  and  governmental  organ- 
izations. 

11.  In  engineering  12.  In  agriculture  13.  In  education 
Name  three  units   which   are 

14.  Artificial  15.  Natural  16.  Semi-artificial 

Give  two  illustrations  of  multipliers  which  are 

17.  Mechanical  18.  Biological  19.  Abstract  20.  Predictive 

21.  Reciprocal  22.  Negative  23.  Branching  or  radiating 

State  the  meaning  of  each  of  the  following  units  and  give  some  of  the 
advantages  resulting  from  its  use. 
24.  A  horse-power  25.  A  watt  26.  A  candle-power 

27.  What  species  of  multiplier  is  implied  in  the  statement  "a  thing  well 
begun  is  half  done"? 

28.  The   driver  of  a   load   drawn  by   six   horses   is   how   many   times   as 
efficient  as  the  driver  of  a  one  horse  load? 

What  primary  principle  of  efficiency  enters  here? 

29.  If  a  microphone  makes  audible  an  otherwise  inaudible  sound,  state  the 
degree  of  efficiency  obtained  by  its  use. 

30.  The  process  of  reducing  two  or  more  fractions  to  a  common  denomina- 
tor means  what  with  reference  to  the  use  of  units? 


UNIT  AND  MULTIPLIER 


55 


What  advantages  result  from  his  process? 

31.  Explain  as  a  case  of  unit  and  multiplier,  the  use  of  a  bolt  on  a  Soot. 

32.  All  the  various  colors  may  be  built  up  by  combining  three  primary 
colors,  viz. :  blue,  green,  and  red.  How  is  the  principle  of  unit  and  multiplier 
here  involved?    What  advantages  result? 

33.  Give  an  example  of  the  multiplication  of  a  loss. 

34.  Give  two  illustrations  of  publicity  as  a  multiplier,  and  state  the  useful 
results  which  have  followed  in  each  case. 

35.  Give  an  instance  where  the  use  of  a  small  unit  and  large  multiplier  is. 
more  advantageous  than  the  use  of  a  large  unit  and  a  small  multiplier.   , 

36.  In  what  respect  is  a  change  of  the  direction  of  one's  motion  a  unit^ 
What  is  the  multiplier  in  this  case? 

37.  Why  is  knowledge  gained  early  in  life  often  worth  many  times  as. 
much  as  knowledge  gained  later? 

38.  State  the  corresponding  principle  with  reference  to  mistakes. 

39.  All  units  used  in  physios  may  be  built  up  out  of  what  three  fundamentat 
units  ?     Illustrate. 

40.  What  is  meant  by  the  dimensions  of  a  derived  unit  in  physics? 
Illustrate. 

41.  Chemically  all  material  objects  are  composed  of  what  units? 

42.  In  fighting  battles  the  method  used  by  Napoleon  on  land  and  that  used 
by  Nelson  on  sea  were  essentially  the  same.  Explain  the  method  and  show 
that  in  effect  it  constituted  an  application  of  the  unit  and  multiplier  principle. 

43.  Explain  the  sense  of  proportion  in  an  observer  as  a  case  of  manifold 
unit  and  multiplier  and  give  two  examples. 


CHAPTER  IV 

THE  GROUP 

Illustration 

Just  as  the  principle  of  reuse  was  enlarged  into  the  broader  and 
deeper  principle  of  the  unit  and  multiplier,  so  the  latter  principle 
may  be  extended  so  as  to  form  a  still  more  general  agent  of  effi- 
ciency, viz. :  that  of  the  group  or  assemblage.  To  indicate  in  a 
brief  way  what  is  meant  by  this,  we  may  continue  an  illustration 
already  used  in  connection  with  reuse  and  the  unit  and  multiplier. 
If  an  orator  preserves  a  speech  and  uses  it  repeatedly,  we  have  a 
case  of  reuse.  If  this  speech  is  published  simultaneously  in  several 
newspapers,  the  method  of  the  unit  and  multiplier  is  employed. 
If  a  number  of  the  orator's  speeches  are  collected  and  published 
together  in  a  volume,  we  have  an  example  of  the  use  of  the  group 
method  as  a  means  of  obtaining  efficiency. 

The  Group  broader  than  the  Unit  and  its  Multiplier 

The  process  of  reuse  implies  a  certain  likeness  in  the  steps  in- 
volved. The  use  of  the  unit  and  multiplier  is  also  a  more  or  less 
homogeneous  process.  But  in  the  group  various  unlike  elements 
may  be  combined  and  treated  efficiently.  Thus  the  combination  of 
various  speeches  in  a  book  facilitates  their  study  and  analysis  as 
a  whole,  as  well  as  their  preservation  and  manipulation  in  libraries. 

Special  Advantages  in  the  Use  of  Groups 

Many  groups  occur  in  a  state  of  nature,  or  appear,  as  it  were, 
of  themselves  in  the  world  about  us,  and  become  immediate  sources 
of  efficiency.  Thus  the  sight  of  a  school  of  fishes  suggests  the 
unit  and  multiplier  method  of  catching  them  by  a  net;  a  collection 
of  workmen  in  a  factory  opens  the  way  to  address  them  all  at 
the  same  time  on  any  given  subject;  the  fact  that  goods  are  packed 
in  barrels  may  enable  some  one  by  quick  handling  to  save  them 
from  being  consumed  in  a  fire. 

A  low  order  of  force  may  often  be  utilized  in  manipulating 
groups.    At  the  same  time  the  idea  of  the  one  and  many  owing  to 

56 


THE  GROUP 


57 


its  great  generality  frequently  operates  in  two  opposite  directions 
(see  direct  and  inverse  groups  on  p.  59).  Even  more  important 
is  the  fact  that  the  character  of  the  ties  which  combine  objects  in 
groups  facilitates  the  building  of  groups  into  extended  systems. 
The  group  method  is  so  flexible  that  it  may  be  used  in  a  crude  in- 
cipient way  and  also  as  a  highly  finished  and  final  instrument  of 
efficiency. 

CLASSIFICATION 
Classification  of  Groups  according  to  Materials 

Groups  may  be  classified  according  to  the  materials  of  which 
they  are  formed.  Thus,  inorganic  groups  are  groups  of  objects 
like  atoms,  bricks,  dollars,  acres. 

Biologic  groups  are  illustrated  by  a  group  of  cells,  a  field  of 
wheat,  or  a  herd  of  cattle. 

Examples  of  social  groups  are  the  family,  a  convention,  or  a 
nation. 

Combinations  of  perceptions,  or  ideas,  are  instances  of  more 
ideal  groups. 

It  is  to  be  noted  carefully  in  this  connection  that  a  group  of 
objects  is  often  closely  connected  with  a  group  of  forces  or  of 
uses.  Thus  in  a  gang  plow  we  have  a  group  of  like  objects  (the 
plow  shares),  and  with  each  use  of  the  plow  the  work  of  the  plow- 
man receives  a  multiplier,  that  is,  is  converted  into  a  group. 

Classification  of  the  Ties  of  Groups 

It  is  also  often  advantageous  to  characterize  and  classify  groups 
according  to  the  ties  which  bind  or  connect  the  elements  compris- 
ing a  group. 

Thus  a  tie  may  be  a  material  thing  like  a  pin,  piece  of  wire  or 
twine,  an  elastic  band,  a  basket,  box,  barrel,  or  dish. 

Also  a  tie  may  be  a  physical  force  of  some  sort  as  cohesion,  gravi- 
tation, or  magnetism. 

Likewise  it  may  be  a  biologic,  psychic,  social,  ethical,  or  religious 
force. 

Ties  may  also  consist  of  some  more  abstract  relation,  as  of  any 
likeness  as  of  color,  size,  weight,  shape,  temperature,  value,  age, 
origin,  development,  feeling,  or  belief,  or  uniformity  in  any  func- 
tion or  relation. 


58  SOURCES  OF  EFFICIENCY 

Special  mention  should  be  made  of  spatial  likeness,  that  is,  of 
concentration  in  space  and  consequent  likeness  of  position.  Some 
of  the  many  advantages  which  often  follow  from  this  species  of 
groupism  will  be  pointed  out  later. 

Of  equal  importance  is  simultaneity,  or  likeness  in  time. 

Concentration  in  both  space  and  time  is  illustrated  by  the  force 
acting  in  the  head  of  an  arrow,  and  in  the  mode  of  action  of  many 
weapons  and  tools,  or  the  force  exerted  by  an  army. 

Special  mention  may  also  be  made  of  the  combinations  of  ob- 
jects in  a  field  of  vision  or  in  a  state  of  consciousness. 

Relation  of  Ties  to  the  Elements  of  Groups 

It  should  be  noted  also  that  in  some  cases  the  tie  is  something 
external  to  the  elements  of  a  group  as  when  objects  are  held  to- 
gether by  a  piece  of  string.  In  other  cases  the  tie  is  in  itself  an 
element  or  in  some  way  embodied  in  an  element  as  when  a  herd  of 
animals  is  held  together  by  one  of  the  number,  or  a  solar  system 
by  its  sun.  From  some  points  of  view  however  an  external  tie 
may  often  be  regarded  as  a  heterogeneous  element  in  a  group. 

Complex  Ties 

The  tie  which  holds  a  group  together  is  often  manifold  or  com- 
plex in  nature.  Thus  when  pupils  are  grouped  in  rooms  in  a  graded 
school,  the  groups  of  pupils  are  determined  not  only  by  the 
walls  and  floors  of  the  building  but  also  by  the  likeness  of  pupils  in 
age  and  development,  and  by  the  leadership  and  control  of  teachers* 
Similarly  a  family  is  bound  together  by  biologic,  psychic,  social, 
ethical,  and  many  different  efficiency  ties. 

It  is  to  be  noticed  also  that  one  tie  may  be  an  aspect  of,  or  may 
lead  to,  another  principle  of  combination.  Thus  cohesion  leads  to 
spatial  concentration;  and  nearness  of  men  in  space  may  lead  to 
likeness  of  dress  or  opinions. 

When  the  tie  which  holds  a  group  together  is  strong  or  feeble, 
temporary  or  permanent,  static,  vibrant,  or  changing,  the  group 
may  be  characterized  accordingly. 

Classification  of  Groups  according  to  their  Forms 

Hence  the  nature  of  the  tie  which  holds  a  group  together  to 
some  extent  determines  the  form  of  the  group.     But  groups  may 


THE  GROUP  59 

take  individual  forms  for  other  reasons,  and  should  often  be  chai;;^ 
acterized  and  classified  according  to  these  forms. 

Thus  a  group  which  contains  two,  three,  or  n  elements  may  be 
termed  a  dual,  triple,  or  n-fold  group  (or  a  duad,  triad,  or  w-ad). 
Similarly  a  group  may  be  large  or  small,  finite  or  infinite.  It  may 
be  one,  two,  or  three  dimensional,  and  may  assume  any  geometric 
shape  whatever. 

An  important  distinction  for  our  purpose  is  that  between  homo- 
geneous and  heterogeneous  groups,  that  is,  groups  composed  of 
like  or  unlike  elements,  respectively. 

It  is  to  be  noted  that  in  determining  the  character  of  a  group  in 
this  respect  much  depends  on  the  point  of  view.  Thus  an  orchard 
viewed  as  containing  apple,  pear,  and  cherry  trees  constitutes  a 
heterogeneous  group,  but  viewed  as  containing  trees  merely  (as 
contrasted  with  corn  stalks,  for  instance)  it  is  a  homogeneous 
group.  In  other  words  by  the  use  of  more  general  ideas,  a  hete- 
rogeneous group  may  often  be  converted  into  a  homogeneous  one. 

Natural  groups  are  those  which  exist  independently  of  any  change 
in  unit  or  tie  wrought  by  human  agency.  Examples  are  the  solar 
system,  a  cluster  of  wild  flowers,  the  petals  in  one  of  the  flowers,  a 
herd  of  wild  animals,  or  a  school  of  fishes. 

Artificial  groups  are  those  which  in  some  respect  have  been 
formed  by  man,  as  a  bundle  of  toothpicks,  or  a  class  of  scholars. 

With  respect  to  order  it  is  useful  to  make  a  distinction  between 
direct  and  inverse  groups. 

A  direct  group  is  one  formed  by  the  inclusion  of  two  or  more 
objects  or  elements  into  one  whole  or  aggregate,  as  when  a  number 
of  objects  are  tied  together  to  make  one  package. 

An  im/erse  group  is  one  formed  by  the  expansion  of  a  single 
object  into  many  forms  or  elements,  as  when  a  grain  of  wheat 
produces  a  number  of  other  grains,  or  a  piece  of  rock  is  separated 
into  its  constituent  elements. 

A  combination  of  the  direct  and  inverse  relations  gives  rise  to 
the  dual-reciprocal  group.  This  consists  of  two  groups  of  elements, 
each  element  in  a  group  being  connected  with  several  or  all  of  the 
elements  in  the  other  group.  An  illustration  is  a  set  of  workmen 
and  a  set  of  tools  so  related  that  any  workman  may  use  any  one  of 
the  tools. 

This  dual  reciprocal  relation  may  be  represented  diagrammatically 


6o  SOURCES  OF  EFFICIENCY 


A. 

ir%     \^  >>      ^^ 

B-\\\  -• 

C-    \Vn 

D- 

\ 

E- 

•1 

2 
3 
4 


by  a  group  of  points  A,  B,  C,  D,  E  (indicating 
workmen),  and  another  group  i,  2,  3,  4,  5 
(standing  for  tools)  and  a  series  of  dotted 
lines  connecting  each  point  in  the  first  group 
with  each  in  the  second.  In  the  diagram  as 
given  in  the  text  only  a  few  specimen  connect- 
ing lines  are  drawn. 

In  this  way  qualities  (or  properties)  may 
be  regarded  as  forming  objects  and  objects 
may  be  analyzed  into  qualities.  This  enables 
us  to  handle  a  group  of  qualities  as  a  single 
object,  Or  a  group  of  objects  by  means  of  a 
common  quality.  Similar  efficient  group  relations  connect  forms 
and  materials;  symbols  and  things;  objects  and  places;  generals 
and  particulars;  principles  and  details;  causes  and  consequences. 
For  one  piece  of  material  may  take  many  different  forms,  and  one 
form  or  mold  may  be  filled  with  many  different  substances;  one 
symbol  may  represent  many  different  objects;  and  one  object  may 
be  represented  by  many  different  symbols. 

By  an  extension  of  the  above  process,  a  number  of  groups  (as  n 
groups)  may  be  combined  to  form  an  w-reciprocal  group.  The 
simplest  form  in  which  this  species  of  group  can  occur  is  that  in 
which  in  a  group  of  n  elements  each  element  in  turn  may  assume 
the  leadership  of  the  remaining  elements. 

Manifold  Groups 

A  group  may  be  manifold  in  the  sense  that  it  may  be  character- 
ized in  many  different  ways.  Thus  a  family  is  determined  as  a 
group  primarily  by  certain  biologic  considerations,  but  it  may  also 
be  determined  by  the  common  physiological  and  mental  peculiari- 
ties of  its  members,  by  the  fact  that  these  members  occupy  the 
same  home,  and  it  is  also  often  an  w-reciprocal  group  because  of 
the  services  which  each  member  renders  to  the  other  members. 

In  concluding  this  portion  of  the  discussion  attention  should  be 
called  to  the  fact  that  reuse  is  a  temporal  group  homogeneous  as 
to  the  quality  of  its  elements ;  and  that  the  unit  and  multiplier  form 
a  group  homogeneous  with  respect  to  both  the  size  and  quality  of 
its  elements. 

EFFICIENCY  FUNCTIONS  OF  THE   GROUP 

To  help  make  clear  that  the  group  should  be  regarded  as  an  in- 
dependent primary  agent  in  obtaining  useful  results,  a  number  of 


THE  GROUP  6l 

the  efficiency  properties  of  the  group  were  pointed  out  and  illus- 
trated in  the  opening  paragraphs  of  this  chapter.  Beside  these 
properties  the  group  principle  has  other  uses  which  invite  special 
attention. 

The  Group  a  Source  of  Economy  and  Reuse 

A  group  means  a  special  field  of  application  for  the  reuse  and 
unit  and  multiplier  principles.  Hence  almost  all  that  has  been 
said  concerning  the  efficiency  functions  of  these  agents  applies  to 
the  group  also.  Grouping  objects  is  also  a  means  of  storing  them 
in  a  small  space  and  finding  them  readily.  Hence  it  means  an 
economy  of  space  as  well  as  of  time.  It  may  mean  an  economy  of 
time  in  other  ways.  When  goods  are  combined  in  packages  they 
can  be  transferred  much  more  rapidly  from  one  place  to  another 
than  if  handled  one  by  one.  This  leads  to  many  other  obvious 
advantages. 

Other  Direct  Uses  of  Groups 

When  objects  are  collected  in  groups  they  may  the  more  readily 
be  protected  from  harm  and  loss.  In  this  connection  also  we  have 
the  proverb  that  in  union  there  is  strength.  The  acquisition  of 
knowledge  is  often  facilitated  also,  since  what  is  true  of  one  member 
of  a  group  is  likely  to  be  true  in  a  measure  also  of  the  other  mem- 
bers of  the  group. 

Transcendent  Uses 

It  is  important  to  note  that  certain  of  the  fruits  of  the  group 
method  are  what  may  be  termed  transcendental,  that  is,  they  are 
qualitative  and  infinite,  and  often,  apparently,  could  not  be  obtained 
in  any  other  way  than  by  the  use  of  the  assemblage  principle.  Thus 
a  number  of  men  by  combining  are  often  able  to  achieve  an  object, 
such  as  building  a  railroad,  which  no  one  of  them  singly  would  be 
able  to  accomplish.  Other  transcendent  results  which  may  follow 
(often  in  an  unexpected  and  dialectic  way)  are  confidence  and 
stimulus  to  the  builders  and  certain  benefits  to  the  public  which 
result  from  the  operation  of  the  road. 

A  mere  improvement  in  a  group  may  lead  to  a  like  series  of 
results,  as  when  an  increase  in  the  number  of  vibrations  in  a  wire 
creates  an  audible  sound,  or  a  concentration  of  the  essential  parts 
of  a  gas  engine  makes  the  aeroplane  possible. 


62  SOURCES  OF  EFFICIENCY 

Complex  Fruits 

Owing  to  the  general  nature  of  the  group  the  various  classes  of 
advantages  connected  with  its  use  often  occur  together  in  a  highly 
complex  and  self -developing  way.  Thus  the  combination  of  many 
small  and  scattered  telegraph  and  telephone  systems  into  one  large 
organization  brings  many  advantages,  as  increased  range  and  fre- 
quency of  use  for  each  instrument,  hence  economy  of  service,  hence 
improved  service,  and  therefore  a  better  development  in  many  ways 
of  the  country  served. 

Many  similar  but  larger  benefits  have  resulted  from  the  union  of 
the  various  states  composing  the  United  States,  with  further  ad- 
vantages such  as  security  from  enemies  and  oppression. 

When  a  number  of  small  rural  schools  are  combined  to  form  one 
large  central  school,  the  pupils  may  be  distributed  in  grades,  fewer 
and  better  teachers  employed,  each  teacher's  work  will  receive  a 
larger  multiplier,  reciprocal  reuse  of  the  combined  libraries  will 
result,  outside  lecturers  may  be  employed,  with  a  dialectic  of  other 
advantages  to  the  various  local  communities  concerned. 

When  a  railroad  is  electrified,  a  large  number  of  locomotives  are 
replaced  by  one  central  power  house.  This  has  the  advantage  of 
replacing  many  engineers  by  one;  that  is,  of  multiplying  the  work 
of  the  engineer  employed.  The  firemen  on  the  locomotives  are  re- 
placed largely  by  mechanical  methods  of  handling  fuel.  The  con- 
centration involved  also  makes  it  possible  to  protect  the  engine  from 
cold  and  loss  of  heat  by  the  use  of  surrounding  walls  and  other 
devices.  It  also  prevents  loss  in  the  form  of  steam  blown  off  when 
a  locomotive  is  standing  still.  Many  other  direct  and  indirect  ad- 
vantages might  be  mentioned. 

As  a  still  more  general  illustration  we  may  consider  the  relation 
of  different  forms  of  energy.  Franklin  identified  lightning  and  elec- 
tricity with  manifest  fruitful  results.  Oersted  went  a  step  further 
and  showed  the  common  nature  of  magnetism  and  electricity  with 
still  further  advantages.  Joule  and  Mayer  advanced  still  further 
and  revealed  the  essential  identity  of  all  physical  forces  as  light, 
heat,  kinetic  energy,  and  electricity.  It  would  take  a  volume  to 
enumerate  the  beneficial  results  which  have  followed  from  this  close 
grouping  of  the  forces  of  nature.  For  the  more  vital  and  compre- 
hensive the  elements  comprising  a  group,  the  greater,  as  a  rule, 
are  the  advantages  following  from  the  use  of  the  group. 


THE  GROUP  63 

Uses  from  other  Points  of  View 

The  value  of  the  group  principle  might  be  made  evident  from 
many  other  points  of  view  as  by  trying  to  realize  what  life  would 
become  without  the  use  of  groups,  or  by  noting  that  the  history  of 
human  progress  has  been,  in  one  respect,  a  history  of  improving 
groupages.  It  is  also  a  help  in  realizing  the  importance  of  the 
group  as  a  source  of  efficiency  to  observe  the  useful  powers  of 
certain  special  forms  of  the  group  principle  as  of  unity,  union, 
concentration,  combination,  cooperation,  etc.  Stating  the  matter 
in  a  more  general  form  we  note  that  every  word  beginning  with  a 
syllable  like  con-,  com-,  col-,  syn-,  syl-,  or  sys-,  stands  for  a 
specifically  realized  group.  Concepts,  for  instance,  are  group  ideas, 
which,  to  use  the  comparison  of  William  James,  are  a  kind  of  seven 
league  boots  carrying  us  forward  in  our  thinking  with  magical 
rapidity  and  ease.  So  groups  in  general  give  wings  to  the  various 
processes  of  life. 

'The  man  who  will  show  me  the  one  in  the  many",  says  Plato, 
'T  will  follow  about  like  a  God."  All  that  mankind  has  learned 
since  Plato's  time  has  but  added  to  the  force  of  his  words. 

Limitations  in  Utilities  of  Groups 

Certain  limitations  in  the  advantages  connected  with  the  use  of 
groups,  or  of  one-in-manynesses,  should  be  mentioned  before  closing 
this  part  of  the  discussion.  Thus  a  very  extensive  unification  fre- 
quently brings  the  drawback  of  stifling  competition  and  often  of 
checking  invention  and  initiative.  A  high  degree  of  concentration 
may  also  increase  the  evil  results  of  error  or  abuse;  that  is,  be  a 
source  of  loss  instead  of  gain.  For  instance,  when  all  the  lights 
of  a  city  are  combined  in  one  electrical  system,  an  explosion  at 
the  central  power  house  may  plunge  the  whole  city  into  darkness. 
Direct  theft  of  a  large  bulk  of  wheat  or  corn  is  almost  impossible, 
but  if  the  value  of  the  grain  be  condensed  into  a  diamond  or  rep- 
resented by  a  signature  written  on  a  piece  of  paper,  such  theft  be- 
comes relatively  easy. 

Hence  the  general  statement  may  be  made  that  groups  owing 
to  their  more  comprehensive  nature  often  lead  to  greater  dangers 
and  losses  than  occur  in  the  application  of  the  reuse  and  unit  and 
multiplier  principles. 


64  SOURCES  OF  EFFICIENCY 

ANALYSIS   AND  DEFINITION 

Comparison  with  Reuse  and  Unit  and  Multiplier 

The  more  or  less  ultimate  sources  of  efficienc)^  in  the  group  and 
its  principal  components  and  characteristics  in  other  respects  have 
already  been  stated  in  the  preceding  part  of  the  chapter.  Thus,  as 
compared  with  reuse  and  the  unit  and  multiplier,  the  group  idea  is 
less  personal,  implies  in  less  degree  the  idea  of  time  and  succession, 
is  more  static  and  more  remote  from  the  idea  of  immediate  gain. 
The  unit  elements  composing  it  may  be  less  uniform,  definite,  and 
homogeneous.  In  a  word  in  its  widest  sense,  the  group  concept  is 
less  concrete  and  hedged  in  by  categories ;  that  is,  is  more  abstract 
and  general. 

Uniqueness  in  the  Group 

It  is  also  to  be  remembered  that  the  group,  like  other  primal 
instruments  of  efficiency,  contains  a  certain  unique  and  character- 
istic essence  which  perhaps  is  largely  beyond  analysis,  and  which 
to  a  certain  degree  is  the  source  of  its  efficiency. 

Definitions 

A  definition,  even  though  it  be  imperfect,  is  often  an  aid  in 
using  a  concept.  We  may  define  a  group  as  a  manyness  which  can 
be  treated  in  some  respect  as  one. 

The  elements  of  a  group  are  the  individual  objects  which  are 
combined  to  constitute  the  group. 

Fundamental  Nature  of  the  Group 

In  the  concept  of  the  group,  or  of  the  one  as  related  to  the  many, 
we  have  what  is  perhaps  the  most  fundamental  source  of  efficiency 
at  our  disposal.  We  obtain  other  approximately  primary  sources  of 
efficiency  by  combining  groups  in  certain  special  ways  or  by  giving 
the  parts  of  a  group  certain  special  forms.  These  additional  primary 
agents  of  efficiency  will  be  treated  in  the  chapters  which  follow. 

METHODS    OF   APPLICATION 

Much  that  was  said  in  previous  chapters  concerning  the  best 
methods  of  utilizing  reuse  and  the  unit  and  multiplier  principle  as 
sources  of  efficiency  applies  to  the  general  group  or  assemblage 
principle.    But  in  connection  with  the  group  as  such  these  methods 


THE  GROUP  6S 

are  often  to  be  modified,  and  in  some  cases  new  principles  of 
method  developed  owing  to  the  peculiar  characteristics  of  the 
group. 

Vast  Number  of  Groups 

For  instance,  in  order  to  make  the  most  efficient  use  of  the 
group,  it  is  important  to  realize  the  vast  number  of  groups  which 
exist  or  may  be  devised.  It  facilitates  this  conception  to  realize  the 
immense  variety  of  elements  which  may  be  combined  in  assemblages, 
the  great  diversity  of  means  by  which  these  elements  may  be  bound 
together,  and  the  many  different  forms  which  groups  as  a  whole 
may  assume.  In  developing  these  conceptions  we  are  aided  by  the 
comparative  freedom  of  the  group  idea  from  limiting  categories, 
and  also  by  the  possibility  of  beginning  with  very  abstract  and  gen- 
eral elements  and  forms,  and  annexing  different  categories,  or  con- 
crete considerations,  singly  or  in  combination,  in  systematic  ways. 

Adaptation  of  Groups 

It  is  also  important  to  study  the  application  of  groups  with  refer- 
ence to  the  different  practical  limitations  which  arise  in  different 
cases.  The  very  great  variety  of  possible  groups  makes  such  study 
necessary  in  order  to  select  the  best  form  of  group  for  any  given 
purpose.  Thus  it  is  desirable  to  know  the  peculiar  advantages  and 
disadvantages  in  each  form  of  concentration  or  unity.  For  ex- 
ample if  the  extent  to  which  magnetic  energy  can  be  concentrated 
in  a  bar  of  soft  iron  had  been  realized  earlier,  the  invention  of  the 
dynamo  would  have  been  accelerated  a  number  of  years.  In  like 
manner  the  knowledge  that  the  energy  contained  in  a  ton  of  radium 
equals  that  contained  in  1,500,000  tons  of  coal  may  some  day  be  of 
immense  direct  practical  importance. 

Symbolism  an  Aid  to  Groups 

In  cases  where  the  unit  objects  under  treatment  must  remain 
scattered  it  should  be  noted  that  the  formation  of  more  or  less 
permanent  groups  is  often  facilitated  by  affixing  some  common 
mark  or  sign  to  elements  belonging  to  a  required  group.  Even 
when  it  is  not  necessary  to  do  so,  it  often  adds  to  efficiency  results 
to  follow  this  method,  as  when  the  soldiers  belonging  to  a  given 
regiment  wear  some  distinguishing  symbol. 


66  SOURCES  OF  EFFICIENCY 

Practice  in  Making  Groups 

Owing  to  the  fundamental  efficiency  importance  of  the  group  it 
is  highly  advantageous  to  practice  forming  groups  on  all  possible 
occasions  till  the  group  habit  is  formed.  In  this  connection  it  is 
important  to  realize  the  many  ways  in  which  the  formation  of 
groups  can  be  aided  by  the  use  of  such  simple  concrete  objects  as 
pins,  elastic  bands,  mucilage,  pigeonholes,  chests  of  drawers,  or  by 
the  use  of  mere  relative  position.  Similarly  it  is  important  to  form 
the  habit  of  making  mental  groups,  as  by  cultivating  the  perception 
of  similarities  and  differences. 

It  may  be  well  to  mention  a  few  of  the  advantages  which  result 
from  the  formation  of  the  group  habit.  We  have  (i)  the  direct 
economies  of  space  used  in  storing  objects;  (2)  the  utilization  of 
groups  by  the  unit  and  multiplier  and  like  methods;  (3)  the  subse- 
quent more  or  less  spontaneous  development  of  individual  groups 
into  systems;  (4)  the  development  of  the  power  quickly  and  easily 
to  improvise  groups  in  any  given  situation. 

Standard  Groups 

Mention  should  be  made  of  the  importance  of  the  thorough 
mastery  and  preferential  use  of  certain  standard  forms  of  groups. 
It  is  often  useful  for  society  in  general  to  employ  such  groups. 
At  the  same  time  each  individual  may  make  special  use  of  certain 
standard  groups  adapted  to  his  personality  and  surroundings. 

Other  things  being  equal  it  is  important  to  use  groups  in  which 
the  elements,  ties,  and  forms  are  as  vital  and  comprehensive  as  pos- 
sible. Thus  mastery  of  a  group  of  the  primary  efficiency  princi- 
ples which  are  under  investigation  will  be  found  to  include  a  host 
of  more  detailed  efficiency  methods.  In  this  connection  it  should  not 
be  forgotten  that  while  a  group  may  on  the  one  hand  be  a  crude  incip- 
ient implement,  on  the  other  it  may  be  a  final  polished  instrument 
giving  unusual  speed  and  power  to  an  efficiency  process. 

Manifold  Groupings 

The  use  of  groups  combined  in  systems  will  be  considered  in  the 
next  chapter.  At  the  present  point,  however,  mention  should  be 
made  of  the  advantage  of  using,  more  or  less  simultaneously,  several 
group  methods  in  a  given  domain  of  material.    Thus  the  process  of 


THE  GROUP  (y-J 

extracting  the  meaning  from  a  book  may  often  be  facilitated  by- 
reading  the  book  backward  or  beginning  at  the  middle,  or  in  va- 
rious scattered  places,  and  employing  special  methods  of  grouping 
the  facts  and  ideas  contained.  This  procedure  not  only  often  brings 
important  economies  but  also  leads  to  many  higher  results.  It  is 
often  useful  to  use  this  method  in  connection  with  a  more  system- 
atic use  of  groups,  as  in  social  or  political  work,  or  in  the  co- 
operation of  the  parts  of  a  large  corporation. 

Definition  of  Efficients 

In  referring  to  the  primary  efficiency  principles  which  we  are 
studying,  it  will  often  be  convenient  to  denote  them  as  a  class  by 
the  term  Efficients.  For  example,  the  primary  agents  of  efficiency, 
or  the  Efficients  studied  thus  far,  are  reuse,  the  unit  and  multiplier, 
and  the  group.  The  adjective,  efficiental,  means  pertaining  to  the 
Efficients. 

Summary  of  Chapter 

A  brief  statement  of  the  ground  covered  in  the  present  chapter 
will  now  be  of  use.  A  still  broader  and  more  fundamental  principle 
of  efficiency  than  either  reuse  or  the  unit  and  its  multiplier  is  the 
group.  Groups  may  be  classified  according  to  objects  composing 
them,  or  according  to  the  ties  which  hold  these  objects  together,  or 
according  to  the  forms  of  the  groups  themselves.  Special  mention 
may  be  made  of  groups  which  are  homogeneous  or  heterogeneous, 
natural  or  artificial,  direct,  inverse,  reciprocal,  or  manifold. 

Groups  are  sources  of  economy  and  new  power  in  ways  additional 
to  those  characteristic  of  reuse  and  of  units.  Hence  the  values  of 
groups  are  correspondingly  more  transcendent  and  complex.  The 
group  is  so  fundamental  in  its  nature  that  the  other  primal  sources 
of  efficiency  may  be  regarded  as  various  methods  of  using  the 
group. 

Here  also  it  is  important  to  realize  the  great  number  of  possible 
groups  and  to  adapt  different  species  of  groups  to  different  uses. 
Especial  attention  is  also  to  be  paid  to  the  use  of  symbolism  in  con- 
nection with  groups,  to  constant  practice  in  their  formation,  to  the 
use  of  standard  groups,  and,  in  some  cases,  to  the  use  of  manifold 
groupings. 


68  SOURCES  OF  EFFICIENCY 

EXERCISE  4 
Give  an  example  of  each  of  the  following  species  of  groups : 

1.  Inorganic  6.  Logical  (or  ideal)  ii.  Complex 

2.  Biologic  7.  Homogeneous  12.  One  dimensional 

3.  Social  8.  Heterogeneous  13.  Two  dimensional 

4.  Mental  9.  Natural  14.  Three  dimensional 

5.  Religious  10.  Artificial 

Give  an  example  of  each  of  the  following  kinds  of  group-making  ties : 

15.  Inorganic  material         18,  Chemical  force  21.  Social  force 

16.  A  living  object  19.  Biologic  force  22.  Religious  force 

17.  Physical  force  20.  Mental   force  23.  Ideal  force 

24.  Give  an  example  of  a  tie  that  is  external  to  the  elements  constituting  a 
group.    Also  to  a  tie  (that  is  embodied  in  one  of  the  elements. 

25.  Give  an  example  of  a  direct  group.  Of  one  that  is  inverse.  Of  dual 
reciprocal  groups.     Of  an  w-reciprocal  group. 

26.  Find  the  degree  of  time  efficiency  in  teaching  a  classi  of  48  persons 
for  an  hour,  as  compared  with  teaching  each  of  the  48  persons  individually 
for  an  hour.    As  compared  with  teaching  them  in  groups  of  16.    Of  8. 

27.  Also  state  the  time  efficiency  of  each  of  the  other  processes  in  Ex. 
26  as  a  per  cent  of  the  first  process. 

28.  Give  an  example  where  a  person's  work  is  multiplied  in  value  by  the 
use  of  a  natural  group  of  some  kind.     By  the  uise  of  an  artificial  group. 

29.  Give  an  instance  where  the  use  of  groups  gives  speed  in  handling 
objects. 

30.  Where  it  saves  property  from  destruction. 

31.  Where  it  results  in  economy  of  the  attention  or  of  other  mental  forces. 

32.  Where  complex  advantages  result. 

33.  Where  a  transcendent  result  is  obtained. 

34.  Give  an  example  of  the  use  of  the  group  method  as  a  crude  initial 
instrument  of  efficiency. 

35.  Also  where  it  is  a  finished,  final  instrument. 

36.  Show  how  the  spinning  jenny  illustrates  the  group  principle  as  a  means 
of  obtaining  efficiency. 

S7.  In  one  day  one  man  by  using  a  common  plow  turned  over  i>^  acres  of 
land.  Another  man  using  a  gang  plow  turned  over  40  acres  in  two  days. 
State  the  degree  of  wage  efficiency  in  the  second  process  as  compared  with 
the  first.  Also  express  the  efficiency  of  the  first  process  as  a  per  cent  of 
the  second. 

38.  Why  should  goods  when  bought  on  a  large  scale  cost  less? 

39.  Combine  8  roses  +  5  lilies  +  6  pinks  into  a  single  group  by  the  use 
of  some  more  general  word  than  those  used  in  the  given  expression. 

40.  Give  two  examples  of  the  advantages  of  concentration  (or  of  the  dis- 
advantages of  separation). 


THE  GROUP  69 

41.  State  the  efficiencies  connected  with  the  use  of  one  comprehensive  elec- 
tric light  system  for  a  city,  instead  of  several  thousand  oil  lamps. 

42.  Give  an  example  where  a  number  of  scattered  and  moving  objects 
are  combined  into  a  group  by  means  of  symbols  or  marks  of  some  kind. 

43.  State  the  advantages  of  the  concentration  of  electricity  in  the  form  of 
high  voltage  on  a  transmission  wire. 

44.  Also  those  in  the  close  alliance  for  a  century  and  a  half  of  the  different 
members  of  the  Rothschild  family. 

45.  Ascertain  the  etymological  meaning  of  the  words  logic,  category,  con- 
sciousness, and  law,  and  show  that  in  the  meaning  of  each  the  group  idea  is 
prominent. 

46.  State  some  of  the  advantages  of  having  those  cells  In  an  organism 
which  perform  the  same  function  collected  in  one  or  two  organs,  as  in  the 
biain,  liver,  lungs,  etc. 


CHAPTER  V 

MULTIPLICATIVE  GROUPS 

Groups  may  be  used  not  only  singly,  but  also  in  combination  in 
the  form  of  extended  systems,  with  a  corresponding  increase  of 
efficiency  results. 

Illustration  of  Multiplicative  Groups 

For  example,  if  the  commanding  general  wishes  a  secret  order  to 
be  conveyed  v.erbally  to  each  soldier  in  his  army,  he  does  not  at- 
tempt to  speak  personally  to  each  individual  in  the  army,  or  even 
to  have  a  messenger  do  so.  The  general  communicates  the 
order  to  his  corps  commanders,  each  of  whom  conveys  it  to  his 
division  commanders,  each  of  whom  transfers  it  to  his  immediate 
subordinates,  and  so  on  till  the  private  soldiers  are  reached.  In  this 
way  the  order  is  conveyed  with  repeated  use  of  the  advantages 
which  characterize  the  group  method,  viz. :  less  labor,  greater  speed, 
practical  simultaneity  of  knowledge,  quickness  and  unity  of  action, 
less  time  for  betrayal,  anH  freedom  for  the  commanding  general  to 
devote  most  of  his  time  and  energies  to  more  important  work  than 
the  communication  of  orders.  In  this  case  the  system  of  groups 
involved  consists  of  the  group  of  corps  commanders,  the  various 
groups  of  division  generals,  and  so  on. 

Diagram  of  Essence  of  a  Multiplicative  Group  System 

To  put  the  matter  in  an  abstract  and  comprehensive  form,  if  we 
have  a  group  of  n  elements  (as  A,  B,  C,  etc.),  each  of  which  is 
connected  with  a  set  of  other  elements  (as  A  with  a,  b,  c)  forming  a 
secondary  group;  each  element  in  a  secondary  group  being  con- 
nected in  like  manner  with  elements  in  a  tertiary  group,  and  so  on ; 
we  have  a  series  of  groups  so  related  that  the  aggregate  may  be 
termed  a  system  of  multiplicative  groups.  This  is  the  instrument  of 
efficiency  to  be  studied  in  the  present  chapter. 

In  the  diagram  the  group  composed  of  the  elements,  A,  B,  C,  etc., 

70 


MULTIPLICATIVE   GROUPS 


71 


is  termed  the  prime  group,  or  the  group  of  the  first  order;  the 

groups  represented  by  a,  b,  c,  and  d,  e, 
f,  etc.,  are  termed  the  secondary  groups, 
or  groups  of  the  second  order;  the  set 
of  groups  which  include  x,  y,  z,  etc.,  are 
of  the  third  order,  and  so  on. 

CLASSIFICATION 

The  various  elements  and  ties  which 
enter  into  the  formation  of  multiplicative 
groups  are,  in  general,  the  same  as  those 
mentioned  in  connection  with  single 
groups  (see  pp.  57-58).  Hence  the  clas- 
sification of  multiplicative  group  systems 
with  reference  to  elements  and  ties,  is 
approximately  identical  with  that  given 
in  the  preceding  chapter  for  groups. 

It  is  different  however  with  the  classi- 
fication of  multiplicative  group  systems 
with  respect  to  the  forms  which  they  may 
assume.  Owing  to  the  more  elaborate 
nature  of  systems  of  groups,  these  sys- 
tems appear  in  certain  important  forms 
which  are  peculiar  to  the  category  of  efficiency  under  investigation. 


Numerical  Species  of  Multiplicative  Groups 

A  multiplicative  group  system  may  be  characterized  by  some 
number  prominent  in  its  structure,  as  by  the  number  of  orders  of 
groups  which  it  contains.  Thus  we  may  have  a  dual  system,  as  a 
group  of  teachers  and  their  groups  of  pupils ;  or  a  3-order  system, 
as  superintendents,  teachers,  and  pupils.  An  important  special  case 
is  that  of  the  infinite  system,  or  one  which  contains  an  unlimited 
number  of  orders. 

A  multiplicative  group  system  may  also  be  characterized  by  some 
standard  number  of  elements  used  in  each  of  the  constituent  groups 
of  the  system.  Thus  the  system  as  pictured  in  the  above  dia- 
gram is  a  grouping  by  threes.  An  important  special  number  form 
is  a  dual  system  in  which  each  group  consists  of  only  two  elements, 
a  positive  and  a  negative  one.     Such  a  system  is  used  in  the  so- 


72  SOURCES  OF  EFFICIENCY 

called  game  of  Twenty  Questions,  where  the  aim  is  to  identify  a 
particular  object  by  twenty  successive  questions  each  of  which  is 
answered  yes  or  no.  What  is  essentially  this  method  is  also  em- 
ployed in  much  detective  work  and  scientific  investigation. 

Spatial  Forms  of  Group  Systems 

Spatially,  multiplicative  systems  may  be  characterized  by  the 
number  of  their  dimensions.  Thus  we  may  have  a  one-dimensional 
or  linear  system.  This  consists  of  a  number  of  elements  arranged 
in  a  line  and  treated  by  some  multiplicative  method.  This  form  is 
so  important  that  it  will  receive  special  treatment  later  (see  p.  76). 

Evidently  also  a  group  system  may  be  two-dimensional  or  areal 
in  arrangement.  By  way  of  illustration  we  have  the  diagram  given 
on  p.  71,  or  a  river  and  its  branches,  or  a  family  tree  as  ordinarily 
diagrammed.  An  important  case  of  somewhat  different  nature  is 
that  of  an  area  divided  and  subdivided  into  parts,  an  example  being 
a  country  divided  into  states,  counties,  and  townships. 

Similarly  a  group  system  may  have  three  dimensions.  An  ex- 
ample is  a  tree  and  its  branches.  An  illustration  of  a  three-dimen- 
sional multiplicative  group  system  of  somewhat  different  kind  is  a 
house  divided  and  subdivided  into  parts  as  rooms,  closets,  shelves, 
drawers,  etc.  Three-dimensional  systems  of  many  special  geometric 
shapes  are  possible  as  cone-shaped,  pyramidal,  spherically  radial, 
and  other  forms. 

It  is  important  to  discriminate  between  group  systems  whose 
parts  are  continuous  or  connected  throughout,  and  those  which  are 
discontinuous  or  made  up  of  parts  more  or  less  separated  in  space. 
An  example  of  the  former  is  a  river  system,  or  a  tree  and  its 
branches.  An  example  of  the  discontinuous  form  is  an  army  as 
organized  into  regiments,  brigades,  and  divisions. 

Other  Important  Forms  of  Multiplicative  Groups 

With  reference  to  the  category  of  time,  multiplicative  group 
systems  may  be  temporary  and  provisional,  or  permanent.  It  is 
often  convenient  to  describe  genetic  or  causal  systems  as  temporal, 
since  they  are  determined  by  factors  acting  in  time.  An  instance 
is  a  family  tree  or  the  consequences  resulting  from  an  event  like 
the  explosion  of  the  battleship  Maine  in  the  Havana  Harbor  in  the 
year  1897. 


MULTIPLICATIVE   GROUPS  73 

As  to  order  we  have  species  which  act  forward  or  backward,  di- 
rectly or  inversely,  by  expansion  or  contraction,  by  synthesis  or 
analysis. 

Systems  of  multiplicative  groups  may  differ  qualitatively  in  in- 
numerable ways.  The  most  important  distinction  in  this  respect  for 
our  purpose  is  that  denoted  by  the  terms  homogeneous  and  hete- 
rogeneous. A  group  system  may  be  homogeneous  (or  heterogen- 
eous) in  several  different  ways,  as  with  respect  to  the  number  of 
elements  constituting  its  individual  groups ;  or  as  to  the  size  or  other 
characteristics  of  the  individual  elements,  or  of  the  ties  binding 
them ;  or  with  respect  to  the  forms  of  the  component  groups.  Thus 
a  telephone  system  is  heterogeneous  for  the  reason  that  part  of  it 
(the  system  of  connected  wires)  is  continuous  and  part  (the  system 
of  keyboards)  is  discontinuous. 

Other  cases  of  heterogeneous  multiplicative  group  systems  are  a 
house  and  its  parts ;  or  the  classification  of  sensations  according  to 
their  quality,  intensity,  and  duration ;  or  a  system  of  transportation 
consisting  of  ocean  steamships,  railroads,  trolley  lines,  automobiles 
or  carriages,  and  human  locomotion. 

Federal  Species  of  Multiplicative  Groups 

Special  attention  should  be  paid  to  certain  important  individual 
forms  of  multiplicative  group  systems.  We  consider  first  what 
may  be  regarded  as  the  normal  or  standard  form;  that  is,  the  best 
form  for  general  purposes.  The  illustration  given  in  the  opening 
paragraph  of  this  chapter  (p.  70)  is  of  this  type.  It  may  be  de- 
scribed as  the  federal  or  hierarchical  species.  It  may  have  one, 
two,  three,  or  n  dimensions,  and  may  often  be  transformed  from  one 
of  these  dimensional  states  into  another.  Other  illustrations  of  it 
are  the  organization  of  the  Roman  Catholic  Church,  or  any  similar 
ecclesiastical,  or  any  political  system  of  government.  Many  busi- 
ness organizations  are  of  the  same  general  type.  For  instance  in 
the  building  trade  we  find  a  combination  of  architects,  contractors, 
foremen,  mechanics,  laborers,  and  apprentices. 

It  is  to  be  noted  that  the  normal  or  federal  type  may  be  either 
continuous  or  discontinuous.  Examples  of  the  latter  are  those 
given  in  the  preceding  paragraph.  Illustrations  of  the  continuous 
or  branching  federal  type  are  a  tree  and  its  branches,  the  gas  or 
water  pipes  of  a  city,  the  nerves,  or  blood  vessels  of  the  human  body. 


74 


SOURCES  OF  EFFICIENCY 


The  use  of  latitude  and  longitude  as  a  means  of  locating  all 
places  on  the  earth's  surface  may  also  be  regarded  as  the  use  of 
a  branching  group  system.  The  same  statement  applies  to  a  sys- 
tem of  coordinates  of  any  sort  as  used  in  mathematics  or  science. 

A  federal  system  may  also  be  continuous  in  certain  parts  or  re- 
spects, and  discontinuous  in  others.  An  instance  is  that  cited  above 
of  a  telephone  system  of  wires  and  keyboards.  An  important  case 
of  somewhat  different  nature  is  that  which  may  be  termed  articu- 
late, as  the  system  of  bones  in  the  human  skeleton ;  or,  more  broadly, 
the  system  of  bones,  muscles,  and  organs  in  the  human  body;  or, 
more  broadly  still,  the  essential  parts  of  every  biological  and  social 
organism.  Articulate  language,  both  oral  and  written,  is  largely 
of  the  same  nature. 

Constitutive  Group  Systems 

The  normal  or  standard  federal  system  may  take  two  other 
contrasted  but  closely  related  forms.  The  first  of  these  is  what 
may  be  termed  the  constitutive  multiplicative  group  form.  This 
consists  of  a  domain  divided  into  certain  major  parts,  each  of  these 
parts  being  divided  into  smaller  parts  and  so  on.  An  example  is 
that  already  given  of  a  country  divided  and  subdivided  into  states, 
counties,  and  townships.  Other  illustrations  of  constitutive  multi- 
plicative group  systems  are  a  city  marked  off  into  wards,  blocks,  and 
houses;  a  library  separated  into  alcoves  and  shelves;  a  book  re- 
garded as  consisting  of  chapters,  paragraphs,  sentences,  and  words ; 
or  a  drama  as  formed  of  acts,  scenes,  lines,  and  words. 

Marginal  Group  Systems 

The  other  of  the  two  species  named  above  may  be  termed  the 
marginal  form.  In  this  type  each  subgroup  is  something  apart  from 
and  attached  to  an  element  in  the  group  above.  Thus  in  the  organiza- 
tion of  the  Roman  Catholic  Church  the  cardinals  are  apart  from 
and  attached  to  the  Pope.  So  in  a  river  system,  or  the  branches  of 
a  tree,  the  smaller  branches  are  apart  from  and  attached  to  the 
larger  branches.  Hence  in  a  marginal  multiplicative  group  system, 
the  tie  which  holds  the  elements  of  a  subgroup  together  is  con- 
tained in  an  element  of  the  next  higher  group;  while  in  a  con- 
stitutive group  the  tie  is  in  some  outside  object  or  some  abstract 
consideration. 


MULTIPLICATIVE   GROUPS      '  75 

A  multiplicative  group  system  may  be  part  marginal  and  part 
constitutive.  Thus  a  railroad  system  (marginal)  may  have  at- 
tached to  it  certain  cities  (constitutive).  So  an  organization  may 
have  the  two  forms  as  parallel  aspects  or  elements.  Thus  we  may 
have  a  continent  subdivided  into  certain  realms  of  ecclesiastical 
jurisdiction  (constitutive)  and  these  districts  governed  by  a  system 
of  church  officials  (marginal).  Similarly  the  area  drained  by  a 
river  system  may  be  regarded  as  divided  constitutively  while  the 
river  system  itself  is  marginal  in  structure. 

Strandal  Multiplicative  Groups 

A  strandal  multiplicative  group  system  is  one  formed  of  linear 
elements  each  of  which  is  subdivided  into  parts  of  different  orders. 
A  system  of  this  kind  may  be  regarded  as  constitutive  from  one 
point  of  view  and  marginal  from  another,  and  hence  is  useful  in 
connecting  one  of  these  two  types  with  the  other.  An  example  of 
the  strandal  type  is  a  river  and  its  branches.  For  in  a  river  system, 
if  the  water  which  enters  each  small  tributary  be  followed  in  its 
course  through  the  larger  branches  and  main  stream  to  the  ocean  it 
may  be  regarded  as  a  continuous  strand  in  the  system,  and  the 
whole  river  system  may  be  regarded  as  a  systematized  bundle  of 
strands,  and  hence  as  constitutive  in  its  nature. 

In  like  manner  if  we  regard  the  trunk  parts  of  a  railroad  system 
or  a  tree  as  manifolded  by  reuse  or  by  swifter  use,  each  of  these 
systems  as  a  whole  may  be  regarded  as  strandal.  Almost  all  mar- 
ginal systems  may  be  analyzed  in  a  similar  way  and  thus  reduced 
to  the  strandal  of  constitutive  form. 

An  important  case  to  be  considered  in 
.,•  ,.        '     .1    .      r  J.-,  .  I  si  Form         2d  Form 

this  connection  is  that  of  the  permuta- 
tions or  combinations  of  a  set  of  ele-  /  ^  AAA 
ments,  as  of  letters  (or  sounds)   which          ,A-<B           AAB 

are  combined  to  form  words.     Thus  an  1       ( C  AAC 

ABA 
array  of  letters  as  first  written  in  the  ,  a  ARR 

accompanying  tabulation  at  the  right  is  A^  B  ■)  B          ABC 

marginal  in  structure.     But  if  the  let-  (  C           ACA 

ters  in  the  higher  groups  be  regarded  as  ACB 

reused  the  array  may  be  rewritten  in  the  I  r  )  R 

second  form,  which  is  essentially  consti-  \q 

tutive  in  nature. 


'je  SOURCES  OF  EFFICIENCY 

The  advantages  connected  with  the  first  method  of  arrangement 
are  certain  economies  as  of  material,  the  more  evident  indication  of 
groupages  to  the  eye,  and  reuse  in  certain  kinds  of  mastery.  The 
advantages  in  the  second  form  are  that  each  completed  strandal 
element,  as  ABA,  can  readily  be  identified  wherever  placed;  that 
consequently  selections  from  such  a  system  may  be  arranged  in 
linear  order  with  any  desired  gaps,  as  in  the  cards  in  a  card  cata- 
logue, or  with  the  words  in  a  dictionary;  or  that  they  may  be  ar- 
ranged in  various  useful  orders  such  as  are  employed  for  instance 
with  the  words  of  a  sentence.  This  brings  us  to  a  fuller  consider- 
ation of  the  linear  type  of  group  systems. 

Linear  Group  Systems 

A  linear  multiplicative  group  system  has  already  been  defined  as 
one  whose  elements  are  arranged  in  a  line.  A  straight  line  itselt 
when  divided  and  subdivided  into  feet,  inches,  and  fractions  of  an 
inch  is  an  example  of  a  constitutive  linear  system.  The  division  of 
time  into  centuries,  years,  months,  days,  etc.,  is  a  similar  instance; 
a  series  of  dots  (or  any  separate  objects)  when  arranged  in  a 
line  and  combined  variously  may  form  a  linear  constitutive  or  a 
linear  marginal  group  system,  according  to  circumstances.  Im- 
portant somewhat  general  instances  of  this  class  are  the  number 
signs  I,  2,  3,  4,  5,  etc.,  written  in  order,  or  the  alphabet  A,  B,  C,  D, 
etc.  It  is  often  an  advantage  to  treat  by  the  linear  multiplicative 
group  method  any  temporal  succession  of  events,  as  thoughts  in 
one's  consciousness,  or  acts  to  be  performed  during  a  given  period 
of  time  as  a  day  or  year.  Similarly,  as  was  illustrated  with  refer- 
ence to  the  above  diagram,  it  is  frequently  a  source  of  efficiency  to 
convert  a  domain  of  material  into  this  form,  as  when  we  arrange 
words  alphabetically  in  a  dictionary  and  are  thus  enabled  to  reuse 
our  knowledge  of  the  order  groupings  in  the  alphabet  in  looking  up 
the  meaning  of  a  word. 

Quite  as  important  as  the  linear  is  what  may  be  termed  the  semi- 
linear,  or  approximately  linear  system  of  multiplicative  groups. 
This  is  a  linear  succession  of  elements  each  of  which  is  somewhat 
areal  in  its  nature. 

Illustrations  of  the  semi-linear  species  are  a  line  of  print,  or  more 
noticeably  the  pages  in  a  book,  a  card  catalogue,  a  succession  of 


MULTIPLICATIVE   GROUPS  '^'j 

states  of  consciousness,  the  notation  of  a  piece  of  music,  or  the 
keys  constituting  the  keyboard  of  a  piano. 

A  group  system  may  be  areal  in  some  parts  and  linear  in  others. 

Two  Principal  T3^es  of  Group  Systems 

Hence,  in  general  we  find  two  principal  types  of  multiplicative 
group  systems: 

The  first  is,  in  the  main,  spatial,  logical,  deductive,  full  of  uni- 
formities, abstract,  a  priori,  and  largely  constitutive. 

The  second  is  dominantly  temporal,  genetic,  branching,  strandal, 
full  of  diversity,  concrete,  a  posteriori,  inductive,  and  largely 
marginal. 

The  federal  system  includes  the  essence  of  both  of  these  types. 

Complex  Group  Systems 

Multiplicative  group  systems  may  be  combined  and  complexed  in 
various  ways.  A  simple  instance  is  the  combination  of  the  root 
system  and  the  branch  system  of  a  tree  by  means  of  a  common 
trunk.  Of  like  nature  are  any  group  systems  of  intake  with  the 
corresponding  system  of  output,  or  related  systems  of  induction  and 
deduction.  Also  two  or  more  systems  may  be  combined  and  used 
in  more  or  less  parallel  fashion  as  an  aid  to  each  other.  Thus  we 
have  the  multiplicative  mechanism  of  a  clock,  corresponding  to 
the  multiplicative  division  of  time  into  parts.  Another  illustration 
is  the  combination  of  an  alphabetical  name  list  and  a  number  list 
to  denote  the  employees  of  some  large  organization. 

Manifold  Mutiplicative  Grouping 

An  important  source  of  efficiency  in  manipulating  a  domain  of 
material  is  a  manifold  multiplicative  grouping  of  the  given  domain. 
A  simple  example  of  this  is  the  multiplicative  grouping  in  one  way 
of  the  parts  of  machine  for  shipment;  and  of  the  same  parts  in 
another  way,  when  the  machine  is  erected  for  use.  So  the  contents 
of  a  book  may  be  grouped  multiplicatively  in  diflferent  ways,  as  by 
chapters  and  also  by  an  index.  The  words  of  a  language  may  be 
grouped  multiplicatively  either  as  parts  of  speech,  or  etymologically, 
or  alphabetically,  or  with  respect  to  likeness  of  meaning  as  in  a 
thesaurus. 

Similarly  the  parts  of  a  country  are  often  grouped  in  various 


78  SOURCES  OF  EFFICIENCY 

multiplicative  ways,  as  by  political  divisions,  by  the  use  of  latitude 
and  longitude,  according  to  elevation  and  drainage,  with  reference  to 
railroad  or  other  transportation  lines ;  by  rainfall,  climate,  resources, 
population,  culture,  and  other  categories.  So  plants  may  be  classi- 
fied according  to  their  uses,  by  lines  of  descent,  or  by  the  technical 
methods  used  by  botanists,  or  according  to  the  color,  size,  and  season 
of  appearance  of  their  flowers. 

A  combination  in  any  given  business  of  what  are  called  line  or- 
ganization and  staff  organization  is  an  important  example  of 
manifold  multiplicative  grouping. 

Similar  illustrations  might  be  cited  without  limit.  For  so  simple 
an  object  as  a  straight  line  may  be  divided  multiplicatively  in  an 
endless  number  of  different  ways. 

Manifold  Reciprocal  Group  Systems 

Manifold  multiplicative  grouping  sometimes  takes  a  form  which 
may  be  termed  reciprocal.  For  example  we  may  form  a  family  tree 
by  taking  an  ancestor  and  tracing  his  descendants ;  or  we  may  form 
a  family  tree  which  spreads  in  the  opposite  direction  by  beginning 
with  a  descendant  and  tracing  his  ancestors  back  through  preceding 
generations.  When  the  same  material  is  treated  thus  in  two  opposite 
directions,  the  result  may  be  termed  a  dual  reciprocal  system.  Such 
systems  may  exist  with  respect  to  a  set  of  objects  and  their  qualities, 
between  forms  and  substances,  generals  and  particulars,  structures 
and  functions,  and  other  similarly  related  pairs  of  categories. 

An  7t-reciprocal  group  system  is  also  possible.  Thus  in  a  domain 
of  n  elements  each  element  may  be  made  the  starting  point  or  apex 
of  a  multiplicative  group  system  which  includes  most  or  all  of  the 
given  n  elements.  This  w-fold  reciprocal  multiplicative  relation 
prevails  more  or  less  among  all  the  individuals  in  a  civilized  com- 
munity; among  a  number  of  cities  connected  by  a  network  of  rail- 
roads, telegraph,  or  telephone  wires.  It  exists  among  the  nerve 
centers  or  even  the  cells  of  the  human  body ;  and  indeed,  in  certain 
ways,  among  all  the  atoms,  ideas,  and  entities  of  the  universe. 

An  important  instance  of  the  species  under  consideration  is  that 
of  scientific  formulas,  or  formula-equations,  such  as  s  =  ^  gt^, 
each  letter  of  which  may  be  given  the  lead  in  turn.     The  result  is 

other  formulas,  as  g  =  ^^  ^nd  t  =  J -??,  each  of  which  represents 

a  useful  aspect  of  the  matter  in  hand. 


MULTIPLICATIVE    GROUPS 


79 


Rectangular  Arrays 

Another  important  case  of  the  w-reciprocal  class  of  multiplicative 
group  systems  is  that  of  a  rectangular  net  work  or  array  of  any  kind, 
as  the  rows  of  corn  in  a  field,  the  trees  in  an  orchard,  a  set  of  pigeon- 
holes, the  streets  in  certain  cities,  the  fibres  of  woven  cloth,  or  the 
strands  in  a  piece  of  wire  netting.  The  manifold  multiplicative  nature 
of  such  arrays  is  illustrated  by  the  fact  that  when  pressure  is  brought 
to  bear  on  any  point  in  a  piece  of  woven  cloth  or  netting,  such 
pressure  is  met  by  a  special  multiplicative  system  of  cohesion  radia- 
ting from  the  point  of  stress. 

Some  combinations  of  group  systems  are  so  complex  that  their 
complete  analysis  into  component  systems  is  difficult  if  not  impossi- 
ble. As  an  example  of  this  we  have  rays  of  light  radiating  from  a 
center,  reflected  or  refracted  by  different  objects,  and  variously  used 
or  transferred  by  them.  Still  more  complex  is  the  organization  of 
the  human  body  and  mind,  or  the  development  of  events  in  human 
history.  It  is  to  be  noted  however  that  in  all  such  complex  systems 
there  appear  spots  and  aspects  of  more  or  less  explicit  multiplicative 
structure  which  are  sources  of  important  efficiencies  in  many  ways,  y 

EFFICIENCY   PROPERTIES   OF    MULTIPLICATIVE   GROUPS 

Since  the  multiplicative  group  principle  is  an  extension  of  the 
group  idea  and  hence  of  the  reuse  and  unit  and  multiplier  principles, 
it  has  the  useful  properties  of  these  preceding  instruments  of  effi- 
ciency in  an  extended  and  pronounced  form.  A  system  of  multi- 
plicative groups  also  has  certain  efficiency  functions  peculiar  to 
itself  and  characteristic  of  its  own  more  developed  nature. 

Economics  due  to  Multiplicative  Groups 

An  application  of  the  multiplicative  group  principle  naturally 
carries  with  it  a  greater  economy  of  material  than  a  single  act  of 
reuse  or  the  employment  of  one  group.  For  instance  reusing  a 
word  by  means  of  a  prefix  saves  the  invention  of  one  new  word; 
but  the  use  of  prefixes  and  suffixes  in  a  multiplicative  group  way  in 
connection  with  a  word  stem  takes  the  place  of  the  formation  of  a 
multitude  of  entirely  new  words.  In  the  machinery  used  in  trans- 
fering  power  in  a  factory,  one  large  wheel  may  be  replaced  by  a 
number  of  small  wheels,  geared  tandem  and  having  an  aggregate 


8o  SOURCES  OF  EFFICIENCY 

weight  which  is  only  a  fraction  of  that  of  the  large  wheel.  This 
economy  of  material  in  the  wheels  leads  to  an  economy  of  space  also 
and  hence  of  material  and  grounds  for  buildings.  A  railroad  system 
which  connects  a  number  of  cities  and  smaller  places  is  usually  con- 
structed as  a  trunk  line  with  a  number  of  branches  and  subbranches. 
It  is  easy  to  see  that  such  a  system  requires  less  roadway  and  material 
of  practically  all  kinds  than  would  be  required  if  each  station  on 
the  whole  road  system  were  connected  directly  with  every  other 
station.  The  same  principle  of  economy  of  material  is  found  in  a 
system  of  telegraph  or  telephone  lines,  and  in  the  blood  vessels  and 
nerves  of  any  organism.  In  fact  this  economy  appears  in  charac- 
teristic ways  in  each  of  the  species  of  group  systems  which  have 
been  discussed. 

The  use  of  a  multiplicative  group  method  and  system  may  also  be 
accompanied  by  a  notable  economy  of  energy.  There  is  a  saving 
of  strength  in  speaking  to  a  number  of  persons  assembled  as  a 
group;  much  greater  then  is  the  economy  which  results  when  a 
message  is  conveyed  through  a  large  system  of  groups  as  in  the 
opening  illustration  of  the  chapter. 

If  the  words  in  a  dictionary  were  not  arranged  in  alphabetic  and 
therefore  linear  multiplicative  group  order  or  in  some  other  system- 
atic way,  in  looking  up  a  given  word  we  should  need  to  look  at 
every  word  in  succession  till  we  came  to  the  desired  word.  Hence 
on  the  average,  we  should  need  to  examine  one  half  the  words  in 
the  dictionary,  and  therefore  go  through,  say,  150,000  items  of  work 
instead  of  5  or  6. 

Similarly  if  the  population  of  the  world  were  not  grouped  multi- 
plicatively  in  some  way  as  in  that  indicated  by  the  address  on  a 
letter,  a  messenger  sent  with  a  letter  to  any  particular  individual 
would  need  to  interview,  on  the  average,  one  half  of  the  people  in 
the  world  before  finding  the  desired  person. 

By  like  methods  it  may  be  shown  that  the  use  of  multiplicative 
groups  often  leads  to  economics  of  time,  space,  money,  and  re- 
sources of  all  kinds. 

Increased  Power  due  to  Multiplicative  Groups 

The  use  of  systems  of  gjroups  leads  not  only  to  diminished  ex- 
penditures but  also  to  an  increase  of  results.    For  instance  by  the 


MULTIPLICATIVE   GROUPS  8l 

use  of  organized  methods  the  products  of  a  farm  may  often  be 
greatly  increased.  By  faciHtating  the  consultation  of  encyclopedias 
and  journals,  the  multiplicative  group  principle  leads  to  an  en- 
larged reuse  of  the  work  of  others  by  any  one  investigator  and 
hence  to  an  augmentation  of  results.  So  in  general  by  making 
communication  and  transportation  of  all  kinds  easy,  the  systematic 
application  of  the  group  principle  increases  the  volume  and  elevates 
the  character  of  reuse  and  multuse. 

A  system  of  multiplicative  groups,  for  many  purposes,  may  be 
regarded  as  a  single  group  of  a  high  order  with  the  efficiency 
properties  as  already  stated  for  the  single  group  correspondingly 
increased.  Examples  are  the  electric  lights  in  a  city,  the  soldiers  in 
an  army,  or  the  citizens  of  a  country. 


Group  Systems  Produce  other  Efficients 

Multiplicative  group  systems  are  also  sources  of  efficiency  in 
more  indirect  ways.  These  may  be  better  realized  if  we  anticipate 
to  a  slight  degree  some  of  the  principles  of  efficiency  to  be  investi- 
gated more  fully  later.  Thus  multiplicative  groups  often  produce 
the  uniformities  or  equivalences  (see  Chapter  VIII,  p.  130)  which 
are  the  basis  of  many  new  single  groups  or  organized  groupages. 
This  may  happen  in  different  ways  as 

( 1 )  By  the  extended  propagation  of  original  data  ; 

(2)  By  discovery  of  the  fact  that  different  domains  contain  or 

are  governed  by  the  same  group  systems ; 

(3)  By  virtue  of  the  power  possessed  by  an  infinite  series  of 

filling  in  a  gap  between  two  widely  separated  or  contra- 
dictory objects. 

These  uniformities  not  only  give  rise  to  new  groupages  but  to 
other  results  which  will  be  presented  in  Chapter  VIII  (p.  130).  An 
illustration  of  these  is  the  fact  that  the  recognition  of  a  common 
multiplicative  group  essence  in  a  tragedy,  a  symphony,  and  a  system 
of  government  may  lead  to  much  marginal  reuse  in  acquainting 
oneself  with  these,  and  obtaining  pleasure  and  profit  from  them. 

MultipHcative  groupages  are  also  sources  of  diversity  in  its 
various  forms  and  hence  lead  to  the  fruits  of  diversity,  such  as 
delicacy  of  motion,  tact,  new  units,  etc.    For  instance  all  machinery 


82  SOURCES  OF  EFFICIENCY 

which  acts  with  fine  gradation  of  power  will  be  found  to  be  charac- 
terized by  a  well  developed  multiplicative  structure. 

Other  similar  illustrations  are  the  deliberation  and  relative  wisdom 
with  which  a  federal  government  acts  as  compared  with  the  sudden- 
ness and  passion  of  a  mob  or  even,  in  many  cases,  of  a  pure  demo- 
cracy.  Likewise  a  multiplicative  grouping  of  religious  beliefs  makes 
possible  a  unity  of  view  in  certain  prime  or  first  group  matters  while 
leaving  freedom  as  to  details,  and  in  this  way  produces  efficiency 
results  of  a  high  order.  An  illustration  of  a  different  kind  is  the 
diversity  of  function  produced  by  the  multiplicative  group  structure 
of  a  wire  netting.  In  such  a  structure  the  economy  of  material  is  so 
great  that  space  is  left  through  which  the  air  may  freely  pass,  while 
flies  and  mosquitoes  are  excluded. 

A  multiplicative  group  system  also  often  opens  the  way  for  cer- 
tain advantageous  directive  processes  (see  Chapter  XI,  p.  192), 
as  for  substitutions  and  exchanges.  Thus  if  the  process  of  making 
a  chair  or  any  other  article  be  grouped  multiplicatively,  certain 
parts  of  the  process  may  be  performed  by  machinery  instead  of  by 
hand,  with  a  great  saving  of  time  and  labor. 

So  certain  primal  parts  of  a  physiological  or  mental  process  may 
become  automatic  or  instinctive;  that  is,  be  performed  by  force  of 
a  low  order  or  even  automatically. 

Results  Not  Otherwise  Attainable 

The  systematic  use  of  the  multiplicative  principle  frequently 
brings  certain  remote  and  unanticipated  results.  Some  of  these 
are  often  unique  and  apparently  otherwise  unattainable.  Thus  in 
the  solution  of  a  mathematical  problem  of  a  certain  kind  the  icx),ooo 
or  more  guesses  and  tests  which  would  be  necessary  if  no  systematic 
method  were  followed  may  be  reduced,  for  example,  to  30  used  in 
successive  groups  of  say  5  each.  Since  a  solution  by  the  former 
method  is  practically  impossible  such  solutions  as  have  been  obtained 
in  the  way  indicated  may  be  said  to  be  due  entirely  to  the  multi- 
plicative group  principle.  Similarly  air  thus  far  has  been  liquefied 
only  by  a  stepping  down  of  temperatures.  So  on  a  vastly  larger 
scale,  if  human  activity  had  not  been  highly  organized  the  existing 
triumphs  of  art,  engineering,  and  science  would  never  have  come  into 
being. 


MULTIPLICATIVE   GROUPS  83 

Complex  Results 

Evidently  the  above  benefits  of  group  organization  may  be  com- 
plexed  in  many  ways.  As  an  illustration  we  have  the  varied  and 
manifold  fruits  of  good  government. 

Values  in  Terms  of  Human  Progress 

The  efficiency  value  of  the  multiplicative  group  principle,  like 
that  of  the  other  Efficients  may  be  presented  in  certain  general  and 
more  or  less  pictorial  ways.  For  example  we  have  the  fact  that 
human  progress  has  been  characterized  and  largely  determined  by 
improving  multiplicative  group  systems.  This  is  true  not  only  of 
civilization  as  a  whole  but  also  of  each  department  of  life  and 
knowledge.  Thus  for  example  mathematics  consists  mainly  of  a 
multiplicative  grouping  of  space  and  quantity ;  psychology  of  a  simi- 
lar grouping  of  mind ;  physical  science  of  a  like  grouping  of  matter 
and  force;  history  of  the  multiplicative  grouping  of  various  data 
with  respect  to  time ;  logic  and  philosophy  of  a  treatment  of  multipli- 
cative groups  as  independent  of  and  underlying  other  categories  as 
far  as  possible.  An  improvement  in  each  of  these  domains  has  meant 
an  improvement  in  its  multiplicative  group  essence.  The  human  eye 
and  ear  are  superior  to  the  other  sense  organs  because  the  former 
contain  superior  multiplicative  group  systems.  Electricity  became  a 
distinct  science  as  soon  as  it  was  developed  into  a  multiplicative 
group  set  of  relations  among  certain  primal  units  and  elements. 

In  human  progress  the  multiplicative  principle  has  also  acted 
in  certain  comprehensive  and  sweeping  ways.  Thus  each  new 
discovery  has  not  simply  added  to,  it  has  multiplied  all  preceding 
achievements. 

Lack  of  Group  Systems  Means  Loss 

The  negative  method  may  also  be  utilized  in  realizing  the  effi- 
ciency values  of  the  principle  of  multiplicative  groups.  The  African 
negro  is  not  lacking  in  many  unit  elements  of  efficiency,  but  his 
life  as  a  whole  in  his  native  land  is  barbarous  because  he  lacks  the 
power  of  forming  any  extended  group  system.  Similarly  if  the 
principle  of  multiplicative  organization  were  eHminated  from  human 
life  in  general,  the  world's  affairs  would  drop  back  many  steps 
toward  chaos. 


84  SOURCES  OF  EFFICIENCY 

Familiar  Words  Showing  Value  of  Group  Systems 

Another  method  of  glimpsing  the  world  of  efficiencies  of  which 
the  multiplicative  group  method  is  the  source  is  that  of  recalling 
the  benefits  connected  with  particular  but  familiar  forms  of  multi- 
plicative groups  such  as  organization,  system,  classification,  co- 
ordination, correlation,  method,  and  order.  Every  progressive  or 
step  by  step  process  is  essentially  an  application  of  the  multiplicative 
group  principle. 

Limitations  in  Utilities  of  Group  Systems 

Before  concluding  this  statement  of  the  uses  of  systematic  group- 
ism,  attention  should  be  called  to  certain  disadvantages  which  often 
accompany  the  application  of  this  principle.  Naturally  the  draw- 
backs connected  with  reuse  or  any  single  group  will  often  appear  in 
an  enlarged  way  when  many  groups  are  used.  But  multiplicative 
group  systems  also  have  peculiar  limitations  of  their  own.  In  the 
first  place  a  multiplicative  group  system  often  means  a  certain 
amount  of  added  machinery  which,  unless  it  is  carefully  used,  be- 
comes an  encumbrance  or  even  a  positive  evil.  Expressing  the 
matter  in  another  way  we  may  say  that  under  certain  circumstances 
it  is  more  efficient  to  use  a  single  large  group  than  a  system  of 
smaller  groups. 

Also  a  multiplicative  group  system  may  be  a  highly  efficient  agent 
in  the  propagation  of  an  evil  act  or  unit  of  any  sort.  Thus  the 
value  of  the  printing  press  has  been  largely  negatived  by  the  de- 
grading purposes  for  which  it  has  sometimes  been  employed. 

An  extended  articulate  machinery  is  exposed  to  other  evils  often 
highly  insidious.  For  instance  in  a  federal  government  where  the 
citizens  choose  certain  representatives,  and  these  select  other  repre- 
sentatives of  a  higher  order,  and  so  on,  at  each  step  of  the  process 
danger  exists  of  forgetfulness,  selfishness,  or  corruption.  So  in 
every  multiplicatively  organized  structure,  weakness  and  danger  are 
connected  with  every  stage  and  method  of  articulation.  It  is  the 
highly  organized  wheat  plant  not  the  simpler  grass  which  is  subject 
to  blights  and  diseases. 

Self-protective  Power  in  Grroup  Systems 

It  is  to  be  noted  however  that  a  multiplicative  group  system  con- 
tains within  itself  certain  means  of  correcting  or  even  preventing 


MULTIPLICATIVE   GROUPS  85 

its  own  defects.  Thus  the  expansiveness  inherent  in  a  multipHcative 
system  gives  a  largeness  of  view  and  grasp  which  tends  to  check 
the  evils  specified  above.  Also  the  multiplicative  propagation  of  an 
error  by  increasing  the  results  of  the  error  quickly  calls  attention 
to  the  error  and  the  need  of  its  correction.  Again,  in  almost  every 
domain  of  material  cross  multiplicative  group  systems  are  possible 
which  tend  to  the  prevention  of  error  and  loss.  Thus  in  forms  of 
highly  developed  representative  government,  not  only  are  certain 
cross-groupings  such  as  the  legislative,  executive,  and  judicial  sys- 
tems already  in  use,  but  others  such  as  the  initiative,  referendum, 
and  recall  are  being  adopted. 

ANALYSIS  AND  DEFINITION 

We  wish  now  to  investigate  the  ultimate  sources  of  efficiency  in 
the  multiplicative  group  principle  in  so  far  as  these  differ  from,  or 
are  an  advance  upon  those  already  found  in  the  single  group.  The 
way  may  thus  perhaps  be  opened  for  increased  efficiencies  in  the 
use  of  multiplicative  groupages. 

Number,  Space,  and  Like  Elements 

Owing  to  the  presence  of  different  orders  of  groups  it  is  evident 
that  in  multiplicative  group  systems  the  element  of  number  is  more 
prominent  than  in  groups  singly  treated. 

The  category  of  space  is  also  more  evident  owing  to  the  stress 
laid  on  the  relative  position  of  the  parts  of  a  system  and  the  result- 
ing shapes. 

The  element  of  order  is  here  also  almost  entirely  new  and  with 
it  some  prominence  is  given  to  the  category  of  time. 

More  emphasis  is  likewise  laid  on  the  category  of  force  for  not 
only  are  elements  bound  together  in  groups,  but  groups  are  held 
together  to  form  higher  groups. 

Efficiental  Elements 

A  group  system  implies  a  certain  uniformity  in  several  ways  as 
among  the  elements  of  a  group  in  relation  to  each  other,  among 
the  groups  which  are  placed  together  in  a  given  order,  and  in  the 
ties  which  bind  elements  or  groups  together.    In  like  manner  differ- 


86  SOURCES  OF  EFFICIENCY 

ences  are  supposed  in,  and  are  a  necessary  part  of  a  system  of 
multiplicative  groups. 

Such  a  system  also  implies  something  outside  of  itself  both  in 
general,  and  also  from  the  particular  fact  that  an  element  may  be 
shown  to  be  a  node  or  point  in  which  several  categories  of  utility 
intersect. 

A  certain  limitation  in  the  nature  of  things  is  also  implied  in  a 
multiplicative  group  system,  for  otherwise  progress  would  be  by  a 
single  instantaneous  step,  and  not  by  progressive  stages.  In  fact 
we  may  regard  each  multiplicative  group  system  as  cut  or  carved  out 
by  an  including  matrix  of  limitations. 

A  system  of  groups  also  differs  from  a  single  group  and  from  a 
mere  unorganized  aggregate  of  groups  by  a  certain  inherent  dynamic 
or  dialectic  property,  which  causes  it  to  act  both  externally  by  expan- 
sion and  internally  by  reorganization  as  in  the  formation  of  im- 
proved units,  ties  and  subgroups,  or  manifold  cross  multiplicative 
groupings. 

Unique  Element 

A  multiplicative  group  system  like  each  of  the  other  Efficients 
contains  something  which  is  unique  and  characteristic;  which  is 
perhaps  beyond  analysis  and  may  be  termed  transcendental. 

Later  we  shall  find  that  most  of  the  constituents  specified  above 
are  themselves  capable  of  a  similar  analysis  into  components.  Our 
analysis  will  then  become  a  multiplicative  expansion  of  constituents 
revealing  a  systematic  array  of  ways  in  which  the  efficiency  princi- 
ple under  consideration  may  be  improved. 

Definitions 

At  this  point  it  may  be  well  to  make  a  brief  statement  of  the 
efficiency  characteristics  of  certain  special  well  known  forms  of 
multiplicative  group  systems. 

Classification  and  coordination  differ  from  multiplicative  groups 
in  general  in  that  they  are  relatively  passive  and  inert. 

Organization  as  such  lacks  the  progressive  orderly  relation  of 
parts  which  is  prominent  in  the  multiplicative  concept. 

The  same  is  true,  to  a  certain  extent,  of  the  idea  of  system. 

For  some  purposes,  a  summary  of  the  results  of  the  above  analysis 


MULTIPLICATIVE    GROUPS  87 

in  the  form  of  a  definition  is  useful.  A  multiplicative  group  system 
may  be  defined  as  a  succession  of  groups,  all  the  elements  in  each 
group  (except  the  highest)  being  closely  connected  with  some  one 
element  in  another  group  (called  a  group  of  higher  order). 

From  another  point  of  view,  multiplicative  groups  form  the  com- 
mon essence  of  organization  and  system,  developed  with  a  view  to 
increased  efficiency. 

METHODS  OF  APPLICATION 

We  shall  next  consider  the  best  methods  of  utilizing  the  principle 
of  multiplicative  groups  as  a  source  of  efficiency. 

Vast  Number  of  Group  Systems 

In  the  first  place,  as  with  the  other  Efficients,  it  is  important  to 
realize  the  great  number  of  forms  which  the  instrument  in  hand  may 
assume.  The  number  of  different  group  systems  is  evidently  greater 
than  the  number  of  different  individual  groups.  For  not  only  may 
the  component  groups  of  a  system  take  various  forms,  but  their 
modes  of  combination  may  also  differ.  It  is  to  be  noted  in  this 
connection  that  one  of  the  best  ways  of  realizing  and  carrying  in 
mind  the  great  diversity  of  forms  which  the  multiplicative  group 
principle  may  assume  is  to  arrange  these  forms  in  a  multiplicative 
way;  that  is  to  apply  the  multiplfcative  group  principle  to  itself. 

Adaptation  in  Application  of  Systems  of  Groups 

Owing  to  the  comparatively  elaborate  nature  of  a  multiplicative 
group  system,  the  selection  of  the  best  form  of  instrument  of  this 
kind  to  meet  any  given  set  of  circumstances  is  of  even  greater 
importance  than  when  dealing  with  single  groups.  Thus  for  in- 
stance the  invention  or  selection  of  the  best  possible  elements  out  of 
which  to  form  a  group  system  often  requires  close  study  to  the  end 
that  the  resulting  instrument  may  be  as  comprehensive  and  mani- 
fold as  possible  in  its  action.  In  general  small  elements  or  elemental 
groups  are  best  adapted  for  this  purpose.  For  example  it  has  been 
found  that  the  individual  rather  than  the  tribe  or  the  family  is  the 
best  unit  for  an  elaborate  social  organization.  Similarly  we  have 
the  atom  or  ion  in  physical  science,  and  the  cell  in  biology.  How- 
ever, immediate  practical  limitations  and  relations  are  often  of  such 


88  SOURCES  OF  EFFICIENCY 

a  nature  as  to  call  for  the  use  of  much  larger  units  than  at  first 
would  seem  desirable.  Thus  the  fact  that  most  men  read  on  the 
average  but  a  small  part  of  each  page  of  a  newspaper  leads  to  the 
use  of  a  large  page  in  order  that  a  reader  may  rapidly  extract  from 
the  paper  what  he  needs. 

As  a  rule  it  is  best  if  possible  to  have  the  component  groups  of  a 
system  contain  as  nearly  as  possible  the  same  number  of  elements ; 
that  is,  to  have  a  multiplicative  group  system  governed  by  a  certain 
dominant  number.  This  is  illustrated  in  the  decimal  system  of  nota- 
tion in  arithmetic,  in  the  metric  system,  and  in  the  use  of  12  as  a  base 
in  certain  relations  of  denominate  numbers.  In  some  cases  a  dual 
system,  especially  one  consisting  of  positive  and  negative  elements 
is  highly  efficient  (see  p.  71).  A  system  of  triads  is  often  used  in 
composing  speeches  or  works  of  art,  use  being  made  of  certain 
standard  triadic  groups  such  as  the  past,  present,  future;  or  data, 
means,  end;  or  theme,  antitheme,  combination. 

The  largest  number  of  objects  which  a  person  can  grasp  simul- 
taneously in  his  field  of  vision  is  said  to  be  7.  Hence  perhaps  we 
have  7  colors  in  the  spectrum  as  it  is  usually  divided,  7  days  in  the 
week,  and  7  intervals  in  the  octave.  These  facts  illustrate  the  im- 
portance of  group  systems  governed  by  the  number  7.  It  is  to  be 
noted  also  that  the  printed  page  is  made  up  of  approximately  40 
symbols,  and  spoken  language  of  40  sounds.  The  more  the  matter 
is  studied  the  greater  is  seen  to  be  the  desirability  of  systems  based 
on  or  utilizing  certain  standard  number  groups. 

Relative  Advantages  in  Different  Species 

It  is  also  important  to  investigate  the  advantages  and  disadvan- 
tages of  each  special  form  of  group  in  other  respects,  and  often  to 
devise  special  forms  adapted  to  peculiar  sets  of  circumstances. 

Thus  the  federal  form  (described  on  p.  73)  has  certain  character- 
istic useful  properties  such  as  the  ease  with  which  it  may  be  grasped 
visually  and  changed  in  case  of  need  into  other  forms. 

In  like  manner  the  linear  species  has  certain  efficiency  functions 
peculiar  to  itself.  In  general  it  corresponds  to  the  linear  habit  of 
consciousness  and  our  method  of  dealing  with  objects  in  time, 
and  its  use  leads  to  reuse  of  those  habits.  Properly  conceived  such 
a  system  may  be  readily  expanded  or  contracted  and  modified  in 


MULTIPLICATIVE  GROUPS  89 

other  useful  ways.  These  advantages  are  illustrated  for  instance 
in  a  card  index. 

The  infinite  series  is  useful  in  bridging  gaps,  in  correcting  or 
preventing  errors,  and  in  other  more  technical  ways. 

Evidently  also  manifold  multiplicative  group  systems,  including 
parallel  and  reciprocal  forms,  have  many  special  uses.  These  func- 
tions may  be  negative,  as  in  preventing  misuse  or  overuse  of  any  one 
form,  or  positive  as  in  supplementing  each  other's  defects  or  in- 
creasing each  other's  efficiency.  Thus  when  the  chemical  elements 
are  systematically  grouped  not  only  according  to  their  atomic 
weights,  but  also  with  respect  to  their  spectra,  and  with  regard  to 
their  useful  properties,  many  checks  on  error  and  many  aids  to 
increased  efficiency  result. 

Frequent  Value  of  Even  Crude  Systems 

In  a  difficult  situation  the  value  of  even  a  crude  multiplicative 
group  method  should  not  be  overlooked.  It  is  also  important  to 
remember  in  such  connections  that  in  view  of  the  large  number 
of  ways  in  which  groups  may  be  formed,  some  sort  of  organized 
group  instrumentalism  is  always  possible.  Thus  in  scientific  inves- 
tigation a  working  hypothesis,  however  temporary  and  provisional, 
prevents  much  aimless  groping  and  frequently,  indeed,  seems  nec- 
essary to  the  attainment  of  definite  results.  So  in  another  field,  the 
Puritan  theology,  however  crude  and  imperfect  it  may  have  been, 
at  least  furnished  a  comprehensive  and  vigorous  system,  and  hence 
perhaps  gave  the  New  England  character  its  sturdy  and  aggressive 
qualities. 

One  is  aided  in  using  relatively  imperfect  systems  with  some 
boldness  because  of  the  fact  that  the  multiplying  principle  is  not  only 
self -corrective,  but  also  self -developing. 

Transformations  of  Multiplicative  Group  Systems 

The  power  to  transform  one  species  of  multiplicative  group  system 
into  another  is  often  an  important  source  of  efficiency.  Frequently 
several  successive  transformations  of  this  kind  must  be  made  to  meet 
successive  changes  in  a  situation.  The  different  evolutions  of  an 
army  during  a  battle  or  a  campaign  are  an  example  of  this  process. 

Standard  units  or  types  of  transformation  of  multiplicative  group 


90  SOURCES  OF  EFFICIENCY 

systems  may  often  be  employed  to  advantage.  An  instance  is  the 
conversion  of  a  fan-shaped  into  a  linear  system.  Another  case  is 
the  transformation  of  a  linear  system  into  a  rectangular  array  (as 
of  pigeonholes)  for  the  sake  of  economy  of  space  and  as  a  means  to 
useful  cross  multiplicative  group  processes. 

Similar  conversions  are  that  of  a  three  dimensional  system  into  a 
two  dimensional  one ;  a  continuous  into  a  discrete  form ;  constitutive 
into  marginal;  heterogeneous  into  homogeneous;  and  the  reverse 
of  each  of  these.  Perhaps  also  it  may  be  said  that  any  one  kind 
of  multiplicative  group  system  may  be  converted  into  any  other. 

Important  special  cases  are  the  various  methods  of  classifying 
persons  by  means  of  their  finger  tips,  with  a  final  reduction  of  a 
branching  system  of  classified  persons  into  a  linear  card  catalogue 
form.  A  process  like  this  is  sometimes  termed  a  lexiconizing  of 
data. 

S3mibolisins  for  Group  Systems 

By  the  principle  of  neighborhood  or  positional  symbolism  to  be 
developed  later  (see  p.  167)  important  special  abbreviations  are 
often  obtainable  in  representing  a  multiplicative  group  system  of 
some  particular  kind.  Thus  in  such  representations  the  symbols  for 
the  higher  groups  in  a  system  may  frequently  be  omitted.  For 
example  in  the  address  on  a  letter,  the  name  of  the  country  is  often 
not  expressed,  and  that  of  the  continent  almost  always  omitted.  The 
great  power  of  the  Linnean  system  of  classifying  biological  species 
is  due  not  only  to  the  fact  that  it  is  a  multiplicative  group  system, 
but  also  to  the  property  that,  owing  to  its  multiplicative  nature,  all 
the  names  involved  except  two,  viz. :  those  for  genus  and  species, 
can  usually  be  omitted.  Similarly  the  name  for  each  human  being 
usually  consists  of  only  two  or  three  words,  and  often  only  the 
initial  letters  of  one  or  more  of  these  words  are  used. 

The  judicious  use  of  symbolisms  not  only  brings  negative  ad- 
vantages in  the  shape  of  economies  of  various  kinds  but  also  a 
dialectic  of  positive  advantages  to  be  presented  more  fully  in  the 
chapter  on  Symbolism  (p.  164). 

Calculus  Methods 

The  simultaneous  use  of  successive  transformations  and  of  adapted 
symbolisms  together  suggest  the  idea  of  creating  certain  group  sys- 


MULTIPLICATIVE  GROUPS  91 

terns  by  calculus  methods.  Such  methods  consist  essentially  in 
obtaining  results  in  a  more  or  less  mechanical  way  by  the  aid  of 
adapted  symbolisms.  Thus  a  problem  in  grouping  like  the  follow- 
ing may  be  proposed  and  solved.  If  250,000  species  of  plants  are 
classified  as  a  multiplicative  group  system  of  9  orders,  on  the  average 
how  many  elements  will  each  group  in  the  system  contain?  The 
solution  of  the  problem  reduces  to  the  solution  of  the  equation 
x^  ^  250,000  and  the  result  obtained  is  ;r  =  4. 

Every  slide  rule  represents  what  is  in  essence  a  multiplicative 
group  system,  and  the  use  of  the  slide  rule  is  largely  a  mechanical 
method  of  manipulation  a  multiplicative  group  system. 

A  study  of  the  efficiency  nature  of  logic  and  mathematics  will 
show  that  these  subjects  constitute  particular  forms  or  applications 
of  multiplicative  group  principles,  and  that  the  calculuses  in  them  are 
therefore  illustrations  of  the  calculuses  possible  in  dealing  with 
group  systems  in  general. 

Ideal  Species  in  Multiplicative  Groups 

Finally  in  this  connection  attention  should  be  called  to  the  impor- 
tance of  keeping  in  mind  at  all  times  the  ideal  system  of  multiplica- 
tive groups  and  of  realizing  this  ideal  as  nearly  as  possible  in  all 
cases.  From  our  point  of  view  this  ideal  species  is  a  multiplicative 
grouping  of  the  Efficients,  by  means  of  the  Efficients,  and  for  effi- 
ciental  ends. 

At  the  same  time  it  is  not  to  be  forgotten  that  for  immediate 
practical  purposes  the  best  general  form  is  the  two-dimensional 
federal  system,  accompanied  by  some  linear  species  as  an  auxiliary. 

From  many  parts  of  the  preceding  discussion  it  is  evident  that  the 
application  of  the  principle  of  multiplicative  groups  will  be  aided  in 
various  ways  by  a  study  of  other  primal  efficiency  agents  in  the 
chapters  which  follow. 

Summary  of  Chapter 

It  will  be  an  advantage  at  this  point  briefly  to  state  results  arrived 
at  in  the  present  chapter.  Simple  groups  may  be  combined  to  form 
groups  which  are  multiplicatively  related  in  various  ways.  The 
different  species  of  group  systems  are  characterized  mainly  by  their 
forms.  Among  the  most  important  of  the  individual  forms  are  those 
termed  linear,  federal,  constitutive,  marginal,  and  manifold.    . 


92  SOURCES  OF  EFFICIENCY 

The  efficiency  functions  of  group  systems  are  those  of  single 
groups  in  a  more  extended  form,  with  other  useful  functions  added. 
Among  these  uses  are  economy  and  delicacy  of  action,  and  great 
intensity  of  force.  Group  systems  also  give  rise  to  or  aid  the  other 
Efficients  in  peculiar  ways.  Multiplicative  groups  also  form  the 
underlying  essence  common  to  all  kinds  of  system,  organization,  and 
coordination.  Hence  a  study  of  multiplicative  groups  should  give  a 
thorough  mastery  of  various  forms  of  system  and  organization. 

In  making  use  of  group  systems,  besides  realizing  their  great  num- 
ber, and  methods  of  adapting  them  to  special  situations,  it  is  im- 
portant to  understand  how  to  use  several  species  of  systems  in 
combination,  and  how  to  transform  one  species  into  another.  Of 
like  importance  is  the  use  of  group  systems  in  connection  with  other 
Efficients.  The  ideal  group  system  is  that  one  in  which  the  com- 
ponent elements  are  the  other  Efficients. 

(EXERaSE  5 

Give  an  example  of  each  of  the  following  species  of  multiplicative  group 
systems : 

1.  Of  three  orders  12.  Constitutive 

2.  Of  more  than  three  orders  13.  Marginal 

3.  Linear  14.  Continuous    marginal 

4.  Areal  15.  Discontinuous    marginal 

5.  Three  dimensional  16.  Rectangular 

6.  Provisional  17.  Dual  reciprocal 

7.  Permanent  18.  N-reciprocal 

8.  Direct  19.  Semi-linear 

9.  Inverse  20.  Conically  expanding 

10.  Heterogeneous  21.  Parallel 

11.  Homogeneous  22.  Manifold 

23.  Complex 

24.  Name  three  natural  multiplicative  group  systems. 

25.  Also  three  artificial  ones. 

26.  Also  three  which  are  part  natural  and  part  artificial. 

27.  Describe  some  system  of  filing  documents  and  explain  this  as  a  form 
of  multiplicative  groups. 

28.  State  the  different  multiplicative  group  organizations  found  in  a  large 
hotel. 

29.  Also  in  a  large  department  store. 

30.  On  a  large  well  managed  farm. 

31.  Explain  the  multiplicative  group  system  used  in  dividing  the  Bible  into 
parts  so  as  to  make  them  readily  accessible. 


MULTIPLICATIVE  GROUPS  93 

32.  State  the  advantages  in  having  the  human  arm  jointed;  that  is,  formed 
of  articulate  parts. 

33.  How  is  the  slowness  with  which  a  clock  runs  down  obtained  and  what 
are  the  advantages   in  this   slowness? 

34.  Why  is  it  that  a  number  containing  only  six  figures  is  able  to  express 
the  result  of  the  most  accurate  measurement  that  man  can  make  by  the  aid 
of  appliances  thus  far  invented? 

Give  an  example  of  a  multiplicative  group  system  which  is  a  means  to: 

35.  Economy  of  material  39.  Uniformity   of    action 

36.  Economy  of  space  40.  Delicacy  of  action 

37.  Economy  of  energy  or  force  41.  Substitution    of   a   cheap   force 

38.  Reuse  for  a  costly  one 

42.  A  transcendent  result 

43.  Give  an  illustration  of  the  drawbacks  which  sometimes  accompany  the 
use  of  multiplicative  groups. 

44.  Napoleon  compared  his  mind  to  a  chest  of  drawers.  State  some  of 
the  advantages  in  a  mind  disciplined  so  as  to  be  usable  in  this  way. 

45.  Is  it  correct  to  state  that  an  organism  is  hig'h  in  the  scale  of  being  in 
proportion  to  the  degree  of  its  multiplicative  group  organization?     Illustrate. 

46.  It  is  said  that  the  commanding  general  of  an  army  sometimes  carries 
in  mind  and  is  able  to  recognize  individually  100,000  soldiers.  Show  how  sys- 
tems of  multiplicative  grouping  may  aid  in  this  process. 

47.  What  are  the  advantages  in  influencing  a  community  by  influencing  its 
leaders  ?  In  correcting  the  evils  in  a  community  by  correctig  the  causes  which 
underlie  these  evils. 

48.  State  some  of  the  various  cross  multiplicative  groupings  used  in  keeping 
a  set  of  business  accounts.  What  are  the  advantages  in  this  manifold  group- 
ing of  accounts? 

Give  two  instances  where  a  multiplicative  group  mechanism  gives 

49.  Concentration  of  force  51.  In  space 

50.  Concentration  in  time  52.  A  high  velocity 

53.  Slowness  of  motion 

54.  Why  does  it  pay  a  railroad  system  to  develop  its  trunk  lines  more 
thoroughly  than  the  branch  lines? 

55.  Show  that  the  efficiency  of  the  insurance  methods  used  in  business 
arises  essentially  from  a  multiplicative  grouping  of  values  and  a  surrender  of 
certain  of  those  of  low  order  that  those  of  high  order  may  be  made  certain. 

56.  To  which  species  of  multiplicative  groups  does  that  belong  which  is 
formed  by  the  banks  outside  of  New  York  City,  their  correspondents  in  New 
York  City,  and  the  New  York  City  clearing  house?  Explain  the  efficiency 
functions  of  such  a  system. 

57.  The  so-called  golden  section  has  been  suggested  as  a  fundamental 
principle  in  esthetics.  Show  that  this  principle  is  essentially  a  special  applica- 
tion of  the  multiplicative  principle. 

58.  State  some  of  the  advantages  which  result  when  the  materials  in  the 


94  SOURCES  OF  EFFICIENCY 

store  room  of  a  factory  are  arranged  according  to  a  multiplicative  group 
system. 

59.  State  some  of  the  advantages  which  have  resulted  from  the  demonstra- 
tion that  all  material  objects  may  be  regarded  as  composed  of  a  few  chemical 
elements    grouped   together   multiplicatively   in    various    ways. 

60.  A  classification  of  the  compounds  of  the  elements  of  carbon,  by  the  gaps 
which  it  revealed  led  to  the  prediction  and  discovery  of  certain  hitherto  un- 
known compounds.    What  species  of  efficiency  result  was  this? 

61.  Show  how  the  multiplicative  grouping  of  knowledge  is  an  aid  to  a  per- 
son both  in  learning  something  about  everything  and  everything  about  some- 
thing. 

62.  State  the  symbolism  for  the  different  orders  in  a  multiplicative  group 
system  used  in  the  following:  3°  7'  5". 

63.  Give  an  example  of  the  transformation  of  a  linear  multiplicative 
group  system  into  an  areal  or  solid  one,  for  the  sake  of  economy  of  space. 
What  other  advantages  result? 

64.  Give  an  example  of  the  transformation  of  a  marginal  multiplicative  group 
system  into  the  strandal  form,  and  point  out  the  advantages  which  result. 

65.  If  500,000  species  of  plants  are  classified  as  a  multiplicative  group 
system  of  8  orders,  how  many  elements,  on  the  average,  will  each  of  the 
component  groups  of  the  system  contain? 

Trace  the  historic  development   of   multiplicative  groups  in   the   field  of 

66.  Education  67.  Politics  68.  Business 


CHAPTER  VI 

ORDERS  OF  MATERIAL 

Illustration 

It  is  often  a  source  of  efficiency  to  substitute  for  a  given  multi- 
plicative group  system  a  series  of  objects  each  of  which  represents 
an  entire  order  of  the  given  group  system.  For  example  it  is 
frequently  convenient  to  represent  an  ecclesiastical  hierachy  by  the 
series,  layman,  priest,  bishop,  archbishop,  cardinal,  pope,  or  by  part 
of  this  series. 

Uses  of  a  Multiplicative  Series  of  Objects 

Such  a  representative  set  of  terms  is  particularly  useful  in  cases 

(i)  Where  it  is  difficult  to  form  or  discover  an  explicit  and  well 

developed  multiplicative  group  system; 
(2)  Where  a  group  system  has  been  so  highly  developed  that  it 
may  be  made  to  assume  a  more  special  and  peculiarly  efficient  form. 

In  these  latter  cases  successive  multiplicative  degrees  of  groupism 
have  become  so  familiar  as  to  have  acquired  the  aggregate  of  useful 
qualities  which  we  often  denote  by  the  term  materiality  or  substance. 
Hence  a  single  object  may  be  used  for  each  order  of  groups,  the 
result  being  a  certain  mechanical  ease  and  simplicity  in  dealing  with 
organizations  and  systems,  though  the  process  is  often  accompanied 
by  compensating  limitations  and  drawbacks. 

In  this  way  we  arrive  at  a  new  principle  of  efficiency,  broader  in 
some  ways  than  that  of  the  multiplicative  group  instrument  and 
narrower  in  others.  This  new  instrument  of  efficiency  we  term 
multiplicative  orders  of  material,  or  more  simply  orders  of  material. 

CLASSIFICATION 
Classification  According  to  Materials 

Multiplicative  orders  of  material  will  be  first  classified  according 
to  the  material  in  which  they  occur  or  of  which  they  are  composed. 
The  first  to  be  considered  are  those  multiplicative  series  found  in 

95 


96  SOURCES  OF  EFFICIENCY 

the  physical  inorganic  world.  An  example  of  such  a  succession  is 
that  formed  by  the  ion  (or  electron),  atom,  molecule,  crystal,  and  a 
body  in  mass.  It  is  important  to  observe  that  in  this  case  as  in  many 
others,  the  progressive  many-to-oneness  may  be  regarded  in  several 
aspects  or  as  the  resultant  of  several  elements,  as  those  of  size, 
number,  force,  and  various  functions.  Another  important  general 
multiplicative  order  in  the  inorganic  world  is  that  of  solid,  liquid,  gas, 
ether.  This  also  is  the  resultant  of  several  elements  of  successive 
groupism. 

The  above  orders  of  material  are  found,  in  whole  or  part,  in 
practically  every  domain  of  inorganic  material.  Each  field  of  work 
in  the  physical  universe  also  usually  furnishes  one  or  more  multi- 
plicative series  peculiar  to  itself.  Thus  in  the  domain  of  astronomy 
are  found  satellite,  planet,  sun,  constellation. 

Those  multiplicative  series  which  occur  in  different  specific  fields 
of  toolage  are  particularly  important  for  our  purpose.  Thus  in 
water  transportation  we  have  the  raft,  rowboat,  sailboat,  steamboat, 
with  subordinate  multiplicative  progressions  connected  with  each  of 
the  given  terms.  The  resultant  series  involved  may  here  be  regarded 
as  one  of  general  efficiency. 

Of  implements  used  in  breaking  up  the  ground  in  agriculture, 
we  have  the  hand,  hoe,  spade,  plow,  gangplow.  Of  instruments 
used  in  reaping  grain  the  multiplicative  succession  is  the  hand,  knife, 
cycle,  scythe,  cradle,  mowing  machine,  reaper,  reaper  and  binder. 
Other  fields  of  work  furnish  like  instances. 

In  the  domain  of  living  organisms  various  important  series  of 
objects  multiplicatively  connected  are  also  found  or  have  been  con- 
structed by  man.  Among  the  instances  which  might  be  cited  are 
cell,  organ,  individual,  society;  bone,  flesh,  blood;  annual,  biennial, 
perennial  plants;  individual,  species,  genus,  family,  order,  class, 
kingdom. 

More  Abstract  Series 

In  the  region  of  mind,  as  to  cognition  the  succession  is  perception, 
memory,  reason;  as  to  emotion,  the  list  is  happiness,  joy,  blessedness, 
In  the  field  of  will  we  find  impulse,  volition,  determination ;  in  that 
of  moral  character  occur  physical  courage  and  moral  courage;  or 
act,  habit,  character,  destiny. 


ORDERS   OF   MATERIAL  97 

The  many  multiplicative  group  systems  in  the  social  and  political 
world  give  rise  to  corresponding  multiplicative  series  of  objects. 
Thus  in  connection  with  the  feudal  system  are  found  serf,  burgher, 
knight,  duke,  earl,  prince,  king.  A  system  of  law  courts  at  the 
present  time  is  presided  over  and  to  a  certain  extent  represented  by 
the  poHce  justice  (or  justice  of  the  peace),  and  by  circuit,  superior,, 
and  supreme  judges.  Many  other  social  and  political  multiplicative 
gradations  will  suggest  themselves  to  the  reader. 

Similarly  multiplicative  series  are  in  use  in  various  more  or  less. 
abstract  worlds.  Hence  we  have  for  instance  such  a  series  with 
respect  to  position,  or  culture,  or  usefulness.  In  this  general  class 
the  most  important  series  for  our  purpose  in  many  respects  is  one 
of  degrees  of  efficiency.  For  instance  a  political  worker  at  first 
must  usually  expend  a  large  amount  of  effort  and  be  satisfied  with 
small  returns.  Later,  after  he  has  acquired  position,  he  may  obtain 
much  larger  results  by  the  mere  utterance  of  a  word ;  and  later  he 
may  produce  still  larger  results  by  mere  unconscious  influence. 

The  most  comprehensive  and  in  many  respects  most  useful  multi- 
plicative series  in  the  world  of  objects  is  the  complex  resultant  one 
denoted  by  the  terms  mineral,  vegetable,  animal,  spiritual. 

Classification  According  to  Form 

Often  also  it  is  an  aid  to  efficiency  to  classify  orders  of  material 
according  to  categories  of  form. 

Thus  some  principle  of  space,  as  that  of  magnitude  for  example, 
may  be  so  prominent  as  to  give  the  series  a  certain  characteristic 
individuality.  For  example  we  may  have  a  multiplicative  series 
determined  mainly  by  the  element  of  sise,  an  example  being  bay, 
gulf,  sea,  ocean.  The  principle  of  relative  magnitude  fixes  the 
different  grades  of  anthracite  coal,  viz.,  rice,  pea,  chestnut,  stove, 
furnace. 

Similarly  we  have  the  different  standard  sizes  of  various  articles 
of  merchandise  and  the  materials  used  in  processes  of  manufacture. 
These  gradations  are  sometimes  due  to  natural  causes  but  more  often 
to  the  commercial  process  called  standardization. 

Important  special  cases  of  quantitative  series  are  the  tables  of 
compound  numbers  as  taught  in  arithmetics.  For  example  in  money 
we  have  the  mill,  cent,  dime,  dollar,  eagle.  Other  like  series  are 
used  in  the  measures  of  weight,  length,  area,  volume,  etc. 


98  SOURCES  OF  EFFICIENCY 

As  to  geometric  form  a  multiplicative  succession  of  objects  is 
-essentially  a  linear  succession  of  points.  Owing  to  the  occurrence  of 
secondary,  or  auxiliary,  or  parallel  series  the  geometric  form  of  the 
series  as  a  whole  may  be  slightly  branching  (or  semi-filiar).  An 
example  is  the  series, 

horse,  trolley,  railroad,  steamboat, 


creeping,  walking,  riding  by   ,   ,  .      , 

(   bicycle,  motor-car,  aeroplane. 

We  here  approach  compound  and  complex  orders  of  material. 

Multiplicative  series  of  objects  may  also  be  characterized  by  the 
element  of  number.  Thus  a  dual  series,  that  is  one  composed  of 
only  two  objects  is  often  comprehensive  and  important.  Examples 
are  the  pairs  of  terms,  appearance  and  reality,  reputation  and  char- 
acter, mind  and  matter,  form  and  substance,  relative  and  absolute. 

Important  triadic  forms  also  occur.  Instances  are  past,  present, 
future;  data,  means,  end;  historical,  psychological,  logical. 

The  series,  simple,  compound,  complex,  is  an  important  one, 
determined  both  by  principles  of  number  and  by  spatial  arrangement. 

A  time  element,  as  that  of  relative  permanence,  may  also  form 
the  most  essential  characteristic  of  a  multiplicative  gradation  of  ob- 
jects. For  instance  in  law  a  written  document  is  on  a  higher  plane 
of  importance  than  verbal  statement,  because  written  words  are 
more  lasting  than  mere  verbal  speech.  So  degrees  of  precedence  in 
time  may,  in  effect,  constitute  a  multiplicative  series.  Thus  we 
have  the  legal  maxim  that  possession  is  nine  points  of  law.  Simi- 
larly preventive  work  is  of  a  higher  order  than  that  which  is  merely 
remedial. 

A  segregative  series  is  one  which  has  arisen  by  the  gradual 
elimination  of  sizes  of  forms  of  objects  lying  between  the  objects 
constituting  the  series.  An  example  of  this  is  the  scale  of  sizes 
of  type  now  used  in  printing. 

Many  other  terms  of  quality  may  be  applied  to  various  orders  of 
material.  Among  these  are  the  words  homogeneous,  heterogeneous ; 
natural,  artificial,  semi-artificial;  positive,  negative;  increasing,  di- 
minishing ;  direct,  inverse ;  contingent,  absolute. 

Some  special  explanation  should  be  made  of  the  last  pair  of  terms 
in  the  above  list.  Owing  to  the  shortness  of  human  life  and  other 
species  of  limitation,  the  gap  between  two  successive  terms  in  a 
progressive  series  may  be  absolute  or  infinite  from  the  efficiency 


ORDERS  OF   MATERIAL  99 

point  of  view.  Thus  in  grading  various  specimens  of  a  given  kind 
of  fruit,  as  of  apples,  all  above  a  certain  size  may  have  a  market 
value  while  all  below  have  no  market  value.  So  in  a  scale  of 
temperatures,  all  within  a  certain  range  may  mean  life,  and  all 
above  the  limit  of  this  range  may  mean  death.  All  the  events  in  a 
certain  future  may  be  accessible  and  under  control,  while  all  in  the 
past  are  beyond  control. 

Complex  Cases 

Complex  orders  of  material  of  many  different  kinds  occur.  Some 
resultant  species  have  already  been  mentioned  and  illustrated. 
Another  instance  is  that  composed  of  the  materials  used  in  making 
a  fire,  as  match,  paper,  kindling  wood,  and  coal,  the  component  fac- 
tors being  size,  inflammability,  duration  and  others  less  conspicuous. 

Similarly  the  stages  of  formal  education  denoted  by  the  terms 
primary,  secondary,  collegiate,  university,  constitute  a  multiplicative 
series  which  is  a  resultant  of  such  factors  as  the  age,  growth,  and 
maturity  of  the  pupil,  and  the  difficulty  and  comprehensiveness  of 
subjects  of  study. 

Probably  every  multiplicative  series  is  in  some  respects  a  resultant 
of  a  number  of  such  series. 

Often  one  multiplicative  series  give  rise  to  another.  Hence 
parallel  series  may  occur.  Thus  side  by  side  with  the  arrangement 
of  bodies  as  solids,  liquids,  gases,  and  the  ether,  we  have  the  senses 
of  touch,  taste  (and  smell),  hearing,  and  vision. 

Groups  of  Orders  of  Materials 

Various  orders  of  material  may  constitute  the  elements  in  a  multi- 
plicative group  system.  Thus  the  different  series  in  the  domain  of 
psychology  may  be  arranged  as  a  multiplicative  system. 

In  like  manner  it  is  often  a  source  of  efficiency  to  develop  in  a 
given  domain  of  material  a  manifold  multiplicative  cross  structure 
of  objects.  For  example  the  different  kinds  of  money  in  use  may 
be  viewed  in  various  serial  ways.  Thus  with  respect  to  relative 
bulk  we  have  copper,  silver,  gold,  paper.  According  to  security  the 
order  is  gold,  silver,  copper,  paper.  Another  arrangement 
could  be  formed  according  to  steadiness  of  value  during  a  given 
period  of  time.     Similarly  the  different  ways  in  which  the  facts  in 


100 


SOURCES  OF  EFFICIENCY 


a  department  of  knowledge  may  be  presented  are  denoted  by  the 
terms  genetic  (or  historical),  psychological  (or  inductive),  and  logi- 
cal (or  deductive),  and  a  multiplicative  series  may  be  developed  cor- 
responding to  each  of  these  terms. 

Different  species  of  multiplicative  gradations  may  also  be  com- 
bined and  complexed  in  various  more  or  less  irregular  ways.  An 
illustration  is  the  aggregate  of  such  series  utilized  in  an  entire 
process  of  education. 

General  Multiplicative  Series 

The  following  tabular  combination  of  multiplicative  series  is  of 
far-reaching  importance  because  of  the  comprehensiveness  of  its 
terms  and  also  because  of  its  specific  applicability  to  many  special 
cases  by  aid  of  slight  variations. 


General   Multiplicative 
Series 

Objective 
Side 

Subjective 
Side 

Material 
Concrete 

Semi-concrete 
Abstract 

Efficiency-abstract 
N 

Iron,  wood,  etc. 
Sound,    color,    ether, 
mechanical    and   bio- 
logical force 
Mind  as  object 
Civilization,    religion, 
etc. 

Categories,    Efficients 
N' 

Muscular   sense 
Vision 

Mind  as  subject 
Reason 

Efficiency   powers 

N" 

The  first  column  of  the  above  table  contains  a  general  succession 
which  is  the  resultant  of  a  large  number  of  efficiency  factors  to  be 
considered  in  some  detail  later  (see  p.  105).  Besides  the  efficiencies 
which  spring  from  the  direct  use  of  the  first  column,  other  useful 
results  are  obtained  by  noting  that  the  actual  use  of  this  column  in- 
volves the  use  of  two  sets  of  factors,  usually  termed  the  objective 
and  subjective  respectively.  Hence  it  is  useful  to  develop  these 
into  two  other  parallel  sets  as  given  in  the  second  and  third  columns. 

It  should  be  observed  that  the  series  mineral,  vegetable,  animal, 
spiritual,  also  corresponds  in  a  general  way  to  that  given  in  column 
*one. 


ORDERS   OF   MATERIAL  lOI 

EFFICIENCY   FUNCTIONS   OF   ORDERS   OF    MATERIAL 

Uses   Compared  with  Those   of   Multiplicative    Groups 

Since  orders  of  material  are  a  modified  form  of  multiplicative 
group  systems,  it  follows  that  the  uses  of  orders  of  material  are 
closely  related  to  those  of  multiplicative  groups.  In  general  the 
efficiency  functions  of  orders  of  material  are  in  some  cases  those  of 
incipient  and  imperfectly  formed  multiplicative  group  systems,  and 
in  others  those  of  final  or  highly  finished  systems. 

Thus  it  has  already  been  pointed  out  that  in  a  field  of  great 
difficulty,  where  an  explicit  group  system  cannot  be  found  or  devel- 
oped, it  is  possible  to  form  an  order  of  materials  which  will  perform 
many  of  the  efficiency  functions  of  a  group  system.  For  instance 
in  the  series  denoted  as  solids,  liquids,  gases,  and  the  ether,  complete 
grasp  of  the  precise  and  fundamental  group  inclusions  involved  is 
lacking,  yet  the  multiplicative  relation  approximated  in  the  series 
is  the  source  of  a  vast  number  of  utilities  and  efficiencies.  Prob- 
ably if  the  multiplicative  principles  contained  should  be  discovered 
and  fully  explained,  the  series  as  stated  above  would  still  continue 
to  be  a  convenient  instrument  by  which  to  handle  the  complex  of 
group  inclusions  involved. 

Economics  due  to  Orders  of  Materials 

The  economy  of  material  which  characterizes  multiplicative  group 
systems  is  even  more  noticeable  in  orders  of  material.  For  in  the 
latter  that  large  fraction  of  a  group  system  which  is  covered  by  an 
entire  order  of  groups  is  represented  by  a  single  object.  Thus  in 
the  series,  individual  person,  man,  mammal,  etc.,  the  word  man  not 
only  includes  the  1,600,000,000  human  beings  now  in  the  world  but 
all  past  and  future  generations  of  men. 

Also  the  use  of  a  multiplicative  series  of  objects  means  an  in- 
creased economy  and  efficiency  of  energy  as  compared  with  the  use 
of  a  corresponding  multiplicative  group  system.  For  owing  to  the 
concretish  nature  of  the  terms  of  a  series  of  objects,  such  a  series 
may  frequently  be  operated  by  a  lower  and  cheaper  order  and  a 
smaller  amount  of  force.  In  other  words  orders  of  material  are 
characterized  by  their  extreme  triggerishness.  The  terms  of  such  a 
series  constitute  handles  or  palpable  means  by  which  to  manipulate  a 
group  system  to  advantage.    In  other  words,  in  this  respect,  an  order 


*    e«0  fl 


I02  SOURCES  OF  EFFICIENCY 

of  objects  is  a  simple  mechanical  tool  by  which  to  handle  a  complete 
far  extended  group  system. 

Other  Characteristic  Efficiencies 

Orders  of  material  often  lead  to  efficiency  in  ways  perculiar  to 
themselves.  The  properties  of  a  series  of  objects  formed  by  stand- 
ardization are  an  example  in  point.  For  example  the  formation  of 
certain  standard  parts  in  the  manufacture  of  automobiles  has  led  to 
large  economies  in  the  manufacture  of  each  of  those  parts,  and  often 
to  important  improvements  in  the  quality  of  the  parts.  Similarly 
the  separation  of  freights  into  different  groups  of  materials  to  be 
carried  by  fast  and  slow  freight  trains  and  by  water  produces  im- 
portant economies  and  efficiencies  in  the  carriage  of  each  of  these 
classes  of  material. 

Orders  of  material  also  often  possess  in  distinctive  form  and  in 
larger  measure  certain  other  efficiency  properties  of  multiplicative 
group  systems  such  as  the  power  of  self-development,  of  utilizing 
auxiliary  quantities,  and  of  opening  the  way  to  directive  work  of  a 
higher  order. 

Fruits  stated  Collectively 

The  efficiency  value  of  orders  of  material  may  also  be  presented  in 
other  more  concrete  and  pictorial  ways.  For  instance  it  may  be 
shown  that  such  series  are  at  work  in  every  highly  developed  depart- 
ment of  life  or  action.  The  building  material  called  concrete  con- 
sists of  the  triadic  series,  gravel,  sand,  and  cement.  A  well  balanced 
system  of  diet  consists  essentially  of  starches,  fats,  and  protein. 
Every  great  work  of  art  contains  the  principle  of  multiplicative 
gradations  in  one  or  more  forms.  Poor  writing,  as  Shakespeare 
says,  is  "words,  words,  words",  that  is,  a  mere  additive  aggregate  ; 
while  good  literature  consists  of  words  and  ideas  in  multiplicative 
relations.  For  example  the  following  couplet  from  Browning 
largely  gets  its  power  from  the  two  multiplicative  series  of  two 
terms  each  which  it  contains : 

"Be  a  god  and  hold  me  with  a  charm ; 
Be  a  man  and  fold  me  with  thine  arm." 

The  efficiency  in  life  insurance  comes  from  the  fact  that  it  trans- 


ORDERS  OF  MATERIAL 


103 


fers  money  (or  resources)  from  a  lower  to  a  higher  stage  of  utility; 
that  is,  from  the  field  of  luxury  to  the  field  of  necessity. 

Values  in  Terms  of  Human  Progress 

Hence  also  it  will  be  found  that  great  men  are  men  who  have 
known  how  to  work  with  or  in  material  of  a  high  order.  In  war 
the  superior  general  by  a  simple  stroke  of  strategy  overwhelms  the 
mere  tactician  however  clever.  So  the  statesman  dominates  the 
politician. 

In  fact  we  may  say  that  the  whole  of  human  progress  has  been 
an  advance  from  stage  to  stage  in  multiplicative  series  fashion. 
Some  of  the  more  important  of  these  stages  are  indicated  in  the 
following  table: 


Stages  in 
General 

Characteristic 
Industry- 

Material   for 
Tools 

Savage 
Barbarous 
Semi-civilized 
Civilized 

Hunting 
Grazing 
Agriculture 
Manufacture 

Wood,  bone,  stone 
Copper,   bronze 
Iron,  steel 
Electrical    machinery 

Human  progress  has  also  been  marked  by  the  use  of  an  increas- 
ing number  of  multiplicative  series  and  by  series  of  a  progressively 
high  order. 


Limitations  in  Utilities 

Along  with  the  advantages  which  come  from  the  appeal  to  our 
sense  of  materiality  or  thinghood  in  orders  of  material,  come  also 
certain  disadvantages  which  must  be  reckoned  with. 

Thus  orders  of  material  are  apt  to  harden  or  fossilize  into  tyran- 
nical forms  which  limit  the  user  of  them  by  their  premature  finality. 
An  extreme  instance  is  the  caste  system  of  India.  A  more  subtle  and 
pervasive  case  is  the  use  of  the  distinctions  between  solids,  liquids, 
and  gases  as  ultimate  and  complete.  A  milder  form  of  this  disad- 
vantage is  merely  a  vague  lack  of  flexibility. 

Also  the  brevity  and  extreme  inclusiveness  in  the  terms  of  a 
multiplicative  series  of  objects  often  leads  to  certain  oversights  or 
distortions  in  the  application  of  such  a  series. 


104  SOURCES  OF  EFFICIENCY 

In  other  words  the  multipHcative  series  as  a  source  of  efficiency 
is  vivid  and  triggerish,  but  often  crude  and  narrow.  It  has  the  de- 
fects of  its  quaUties. 

The  orders  of  material  which  characterize  our  system  of  juris- 
prudence furnish  illustrations  of  what  has  just  been  said.  The 
careful  gradation  of  crimes  and  the  formulation  of  a  certain  succes- 
sion of  definitions,  precepts,  maxims,  and  laws,  are  most  useful 
where  so  many  varied,  conflicting,  and  often  selfish  interests  con- 
verge as  in  the  realm  treated  by  jurisprudence.  On  the  other  hand 
many  of  the  distinctions  and  standards  involved  are  more  or  less 
artificial  and  leave  the  way  open  to  numerous  errors  and  abuses. 

ANALYSIS  AND  DEFINITION 

Comparison  with  Multiplicative  Groups 

In  orders  of  material  as  compared  with  multiplicative  group  sys- 
tems, ties  and  forms  recede  into  the  background  while  unit  elements 
become  prominent. 

Also  the  concept  of  number  is  more  specific  and  distinct,  as  is  also 
that  of  order. 

With  respect  to  force  or  energy,  we  may  say  that  the  multiplica- 
tive series  is  more  static  and  passive ;  that  is,  it  constitutes  a  near  and 
familiar  but  not  always  aggressive  toolage. 

Appearances  often  Deceptive 

It  is  also  to  be  carefully  noted  in  this  connection  that  an  order  of 
objects,  while  it  is  essentially  multiplicative  in  nature  and  action,  is 
often  additive  in  appearance.  Thus  when  we  climb  a  mountain  our 
steps  are  additive  in  that  each  step  increases  our  elevation  above 
the  sea  level  by  the  same  amount;  but  at  the  same  time  each  new 
step  increases  the  area  of  vision  in  a  multiplicative  way.  Similarly 
equal  increments  in  temperature  may  produce  multiplicative  changes 
in  any  given  material.  If  the  radius  of  a  circle  be  divided  into 
equal  parts  the  areas  of  the  corresponding  circles  form  a  multiplica- 
tive succession,  and  a  like  property  holds  for  the  sphere  and  other 
solids.  Hence  it  is  important  to  remember  that  vital  efficienc> 
properties,  not  mere  outward  appearances,  determine  whether  a 
given  set  of  objects  form  a  multiplicative  succession.  We  here 
glimpse  from  another  point  of  view  the  fact  that  the  multiplicative 


ORDERS  OF  MATERIAL 


105 


series   contains    its    own    characteristic   sources    of    efficiency    and 
hence  possesses  a  characteristic  uniqueness  and  individuality. 

Each  particular  form  of  multiplicative  series  is  capable  of  its  own 
special  analysis.  The  dual  series  denoted  by  the  terms  concrete  and 
abstract  is  so  important  and  frequently  used  that  it  seems  desirable 
to  try  to  determine  its  efficiency  meaning  as  exactly  as  possible. 
This  is  best  done  by  considering  the  relation  of  the  terms  concrete 
and  abstract  to  certain  other  more  or  less  elemental  categories  of 
efficiency. 

Meaning  of  Concrete  and  Abstract 

With  respect  to  mind,  the  concrete  relates  primarily  to  the  senses, 
the  abstract  to  the  reason. 

In  relation  to  force  or  energy,  the  concrete  is  that  which  has  been 
thoroughly  assimilated  and  reduced  to  the  mechanical  trigger  state. 
Thus  we  cannot  help  seeing  a  red  color,  or  feeling  a  pain  when 
touched  by  a  piece  of  very  hot  iron ;  the  color  red  and  hot  iron  are 
accordingly  termed  concrete. 

With  regard  to  space  the  efficiencies  embodied  in  the  concrete  are 
more  special,  local,  and  individual. 

With  respect  to  uniformity,  the  abstract  possesses  in  higher  degree 
special  properties  of  continuity,  uniformity,  and  equivalence,  as  will 
be  indicated  more  fully  in  Chapter  VIII. 

In  relation  to  the  group  principle,  the  concrete  tends  to  form  the 
elements,  especially  those  of  lower  order,  and  the  abstract  to  form 
elements  and  groups  of  higher  order  and  ties  of  all  groups  but  more 
particularly  those  of  higher  order. 

With  respect  to  limitation,  the  concrete  is  more  subject  to  limita- 
tion as  we  ordinarily  understand  the  term.  Thus,  for  instance,  that 
species  of  limitation  which  we  call  impenetrability  is  prominent  in 
material  and  concrete  things.  Two  material  objects  cannot  occupy 
the  same  portion  of  space  at  the  same  time,  but  two  geometric  dia- 
grams may  do  so.  In  like  manner  a  material  object  cannot  be  in 
two  places  at  the  same  time,  but  it  is  possible  for  an  idea  to  be 
simultaneously  in  a  multitude  of  places.  An  acre  of  land  cannot  be 
owned  simultaneously  by  two  persons,  but  the  same  view  of  life 
may  be  possessed  by  many  persons. 

In  that  more  advanced  or  pronounced  form  of  the  abstract  which 


Io6  SOURCES  OF  EFFICIENCY 

we  have  termed  the  efficiency  abstract,  the  entities  involved  are  still 
freer  from  limitation  than  those  included  in  the  conventional  ab- 
stract, and  consist  essentially  of  the  Efficients  themselves. 

In  the  table  on  p.  lOO,  by  N  we  mean  any  possible  sources  of 
efficiency  beyond  the  Efficients  themselves.  Hence  from  our  point 
of  view  the  term  metaphysics  means  sources  and  modes  of  efficiency 
beyond  concrete,  physical,  or  phenomenal  ones.  Hence  N  stands  for 
any  possible  and  as  yet  unexplored  region  of  efficiency. 

Definition 

Under  certain  circumstances,  the  following  general  definition  will 
be  found  useful.  By  the  term  multiplicative  order  of  objects  is 
meant  a  series  of  objects  each  of  which  has  a  certain  multiplicative 
relation  to  the  preceding  object  in  the  series. 

METHODS  OF  APPLICATION 

Number  of  Species 

The  order  of  materials  and  multiplicative  group  principles  are  so 
closely  related  that  much  which  was  said  in  the  preceding  chapter 
concerning  the  best  methods  of  using  multiplicative  group  systems 
applies  also  to  orders  of  material.  Thus  the  great  number  of  differ- 
ent multiplicative  series  of  objects  is  evident  from  the  fact  that 
possible  systems  of  multiplicative  groups  are  so  numerous. 

Adaptation  to  Individual  Situations 

It  also  follows  that  it  is  important  in  given  circumstances  to  try  to 
determine  the  best  available  gradation  of  materials  and  often,  if 
possible,  to  discover  and  utilize  some  hidden  series  of  this  kind  in  a 
given  field  of  work.  For  example,  in  taking  physical  exercise  it  is 
an  advantage  to  realize  that  gradations  of  efficiency  exist  in  methods 
of  exercise,  and  that  the  most  effective  forms  for  mature  persons 
are  those  which  with  least  effort  produce  a  free  circulation  and 
change  of  position  of  the  fluids  of  the  body. 

To  use  another  illustration,  in  an  approximately  rectangular 
room  the  furniture  and  ornaments  may  be  arranged  in  a  variety  of 
artistic  ways,  but  in  a  room  of  irregular  shape  they  may  usually  be 
arranged  only  in  one  best  way.  Hence  the  former  shape  is  broadly 
speaking  on  a  higher  plane  of  excellence. 


ORDERS  OF  MATERIAL  107 

Emphasis  on  the  Higher  Terms  in  a  Series 

In  using  orders  of  material,  in  almost  all  cases  it  is  a  source  of 
increased  efficiency  to  lay  particular  stress  on  the  higher  terms  in 
the  series.  Hence  arises  the  prime  value  of  knowing  and  controlling 
centers  of  influence,  strategic  points,  psychological  moments,  under- 
lying causes,  means  of  communication,  and  transportation  routes. 

Hence  also  the  importance  of  the  love  of  art  for  art's  sake,  or  of 
truth,  or  of  any  source  of  efficiency  for  its  own  sake. 

Hence  again  the  supreme  importance  of  clinging  to  fundamental 
ethical  or  other  principles  in  times  and  places  of  unusual  difficulty. 

This  principle  of  efficiency  is  also  applicable  to  many  of  the  details 
of  life.  Thus  the  wise  traveller  frequently  makes  sure  that  his 
money  is  in  good  shape.  So  the  writer  who  desires  to  be  clear  and 
forcible  is  at  pains  to  use  in  the  most  effective  way  the  particles 
which  denote  time,  space,  and  other  prime  groups,  notwithstanding 
the  apparent  insignificance  of  such  words. 

Importance  of  Dual  Series 

It  is  also  well  to  note  and  take  advantage  of  the  great  power 
inherent  in  fundamental  dual  series  such  as  those  denoted  by  pairs 
of  terms  like  objective  and  subjective,  concrete  and  abstract.  Even 
the  baseball  player  makes  use  of  this  principle  when  he  recognizes 
the  superior  value  of  what  he  calls  "inside  baseball". 

Self-corrective  Power 

In  using  multiplicative  series  of  objects  it  is  also  desirable  to  keep 
in  mind  the  fact  that,  owing  to  the  power  of  self-correction  which 
characterizes  them  as  well  as  multiplicative  group  systems,  even  a 
crude  series  may  often  be  used  aggressively. 

Groups  of  Series 

Efficiency  in  the  application  of  the  principle  in  hand  is  often  much 
increased  by  dealing  with  orders  of  material  in  groups,  or  even  as 
group  systems.  In  this  connection  orders  of  material  propagated 
from  some  central  form  of  series  are  of  especial  importance.  Thus 
the  series  denoted  by  the  terms  solid,  liquid,  gas,  ether,  gives  rise  to 
the  sense  perception  series  indicated  by  the  words  touch,  taste,  hear- 
ing, vision;  also  to  a  progressive  set  of  terms  denoting  the  sources 


Io8  SOURCES  OF  EFFICIENCY 

of  artificial  light,  viz.:  tallow,  oil,  gas,  electricity;  also  to  the  modes 
of  transferring  heat  indicated  by  the  terms  conduction,  convection, 
radiation. 

Another  example  of  parallel  series  is  the  following :  country,  conti- 
nent, planet;  local,  continental,  planetary  winds;  tornado,  cyclone, 
monsoon. 

Symbolisms 

Certain  efficient  symbolic  methods  of  denoting  a  higher  term  in  u 
multiplicative  series  are  already  in  use.  Thus  suffixes  like  -age, 
-ism,  and  -ize  cause  a  particular  word  to  have  a  general  meaning. 
Examples  are  the  words  symbolism  and  symbolize  as  compared  with 
the  word  symbol.  Similarly  a  higher  order  of  material  is  sometimes 
expressed  by  use  of  a  noun  in  the  singular  instead  of  the  plural 
form.  An  illustration  is  honor  as  contrasted  with  honors,  or  profit 
with  profits. 

Other  symbolic  devices  to  obtain  a  like  end  are  the  use  of  italics, 
or  of  capital  letters  of  various  sizes  and  kinds,  emphasis  in  oral 
speech,  the  use  of  gestures,  etc.  Evidently  many  other  forms  of 
symbolism  might  be  invented  to  indicate  multiplicative  gradations. 

Ideal  Species 

With  orders  of  material,  as  with  the  other  Efficients,  it  is  impor- 
tant to  conceive  of  an  ideal  form  and  to  make  the  utmost  use  of  it  in 
various  ways  including  approximate  and  marginal  uses. 

For  our  purpose  this  ideal  form  is  a  series  of  efficiental  terms 
used  for  efficiental  ends. 

Summary  of  Chapter 

The  present  chapter  may  be  briefly  summarized  as  follows.  It  is 
advantageous,  in  certain  connections,  to  condense  an  extended  group 
system  into  a  simple  succession  of  objects,  each  of  which  forms  a 
highly  economical  representation  of  a  whole  layer  or  order  of  the 
given  system.  Frequently  such  a  multiplicative  series  of  representa- 
tive objects  arises  or  comes  into  effective  use  in  a  given  domain 
before  any  explicit  group  system  has  been  worked  out  in  this  domain. 
Also  such  a  multiplicative  series  may,  at  times,  be  the  resultant  and 
representative  of  several  group  systems. 


ORDERS  OF  MATERIAL  109 

As  to  its  form,  every  multiplicative  series  essentially  constitutes  a 
line  of  objects,  but  from  other  points  of  view,  a  great  variety  of  kinds 
of  series  exist,  owing  to  the  fact  that  such  successions  of  objects  are 
found  in,  or  may  be  devised  for,  each  domain  of  material  or  de- 
partment of  knowledge. 

On  the  one  hand,  orders  of  material  are  sources  of  efficiency  owing 
to  the  extreme  inclusiveness  of  each  object  in  such  a  series,  and 
owing  to  the  adaptability  of  these  objects  to  directive  management. 
On  the  other  hand,  because  of  the  comprehensiveness  of  these  series, 
they  are  especially  adapted  to  deal  simply  and  effectively  with  com- 
plex data  such  as  the  stages  of  human  progress. 

In  making  use  of  multiplicative  series,  especial  care  is  to  be  taken 
to  grasp  their  great  number,  to  realize  partially  hidden  or  deceptive 
species,  and  to  lay  emphasis  on  those  terms  which  are  high  in  a  given 
series. 


EXERCISE  6 

State  the  class  or  classes  to  which  each  of  the  following  orders  of  material 
belongs : 

1.  Steel  frame,  brick,  wood,  trimmings  (as  found  in  a  modern  office  build- 
ing). 

2.  Percepts,  concepts,  ideas,  laws. 

3.  Imitation,  invention   (or  discovery),  creation. 

4.  Farm,  township,  county,  state,  country,  continent. 

5.  Fashion,   principle. 

6.  Pint,  quart,  peck,  bushel. 

7.  Water,   blood. 

8.  (Chemistry)  o      u  ,         S^rt  ]      (Philosophy) 
jphysics      J    ^^°^°Sy,  Psychology  JjS,^^.^^^^y|     JReligion      j 

9.  Bonds,  preferred  stock,  common  stock. 

10.  Standard,  choice,  fancy,  extra  fancy  (as  terms  for  grades  of  fruit). 

11.  Shell  life,  nest  life,  wing  life  14.  Physical  courage,  moral  courage 

12.  Food,  offspring,  culture  15.  Hand  craft,   brain  craft 

13.  Starch,   fat,  protein  16.  Property  rights,  human  rights 

17.  Give  a  multiplicative  series  of  six  terms  concerning  periods  of  time  of 
different  lengths. 

18.  Give    the    multiplicative    series    of    implements    whose    function    is    to 
thresh  grain. 

19.  Give  a  multiplicative  series  of  velocities  in  practical  use. 

20.  Of  weapons  used  in  war. 

21.  Of  states  in  the  United  States  with  respect  to  area. 


no  SOURCES  OF  EFFICIENCY 

Give  an  illustration  of  an  order  of  materials  which  is 

22.  Artificial  23.  Natural  24.  Resultant 

Give  an  illustration  of : 

25.  Two  or  more  orders  of  material  which  are  parallel. 

26.  Of  manifold  cross  orders  of  material. 

27.  Give  an  illustration  of  an  order  of  materials  used  in  some  business 
as  a  result  of  the  process  of  standardization. 

28.  Of  an  order  of  materials  that  is  additive  in  appearance  but  is  multiplica- 
tive  in  essence. 

29.  Name  a  series  of  well  known  plateaus  which  are  respectively  Yi  mile, 
I  mile,  2  miles,  5  miles  above  sea  level.  Taken  with  a  piece  of  land  close  to 
sea  level  in  what  respect  is  this  an  order  of  materials. 

30.  Give  an  illustration  of  the  difference  between  concrete  and  abstract 
utility. 

31.  Point  out  the  advantages  involved  in  being  right  handed  (or  left 
handed),  instead  of  ambidextrous. 

32.  Give  two  illustrations  of  the  advantages  of  using  abstract  number  in 
arithmetic. 

33.  Also  of  the  utility  of  abstract  words  in  language. 

34.  If  a  given  process  be  divided  into  a  multiplicative  succession  of  parts, 
in  carrying  out  this  process  it  is  made  easy  to  stop  when  any  required 
degree  of  accuracy  has  been  obtained.  What  economies  or  efficiencies 
result?    Illustrate. 

35.  From  the  order  of  materials  standpoint  explain  the  efficiency  meaning 
of  the  statement  "What  one  does  not  have  in  the  head,  one  must  have  in 
the  heels". 

36.  What  order  of  materials  is  implied  in  the  statement  "strike  me,  but 
hear   me". 

37.  State  as  fully  as  you  can  the  principles  of  efficiency  involved  in  the 
term  "psychological  moment". 


CHAPTER  VII 

EXTERNALITY 
Illustration 

It  was  remarked  in  Chapter  II  that  an  epoch  in  human  progress 
occurred  when  some  primitive  manHke  creature  first  hit  upon  the 
device  of  saving  labor  by  keeping  and  using  again  a  club  which  he 
had  found  helpful  in  procuring  food.  It  was  a  still  earlier  and  per- 
haps more  important  epoch  in  efficiency  history  when  a  club  was 
used  for  the  first  time  without  any  thought  of  its  repeated  use;  or 
when  any  external  object  was  first  used  by  some  animal  as  an  aid 
in  obtaining  food  or  protecting  itself  from  its  enemies,  an  illustration 
being  the  use  of  a  web  by  a  spider. 

General  Statement 

This  explicit  use  of  an  object  or  objects  external  to  a  given 
domain  as  a  means  of  obtaining  results  constitutes  the  next  primal 
instrument  for  obtaining  results  which  we  shall  investigate.  This 
source  of  efficiency  often  takes  puzzling  and  extreme  forms.  This 
fact  is  illustrated  by  various  statements  in  common  use  such  as 
"The  longest  way  round  is  the  shortest  way  home",  "There  is  a 
point  where  economy  becomes  wasteful  extravagance",  and  "There 
is  that  which  scattereth  and  yet  increaseth".  These  as  well  as  other 
aspects  of  the  matter,  show  the  need  and  value  of  careful  study  of 
the  method  of  obtaining  results  which  is  under  consideration. 

The  principle  of  efficiency  involved  in  the  use  of  objects  or  entities 
external  to  oneself  or  to  a  given  domain,  we  term  externality. 

CLASSIFICATION 

Objects  Usable  as  Externalities 

As  to  the  objects  which  may  constitute  an  externality,  we  may  say 
in  general  that  any  object  may  be  used  as  an  auxiliary  means  to 
efficiency  in  some  way  or  ways,  but  not  in  all  ways.  Thus  the 
moon  has  often  been  an  aid  in  determining  the  position  of  a  ship  at 
sea,  but  the  rocks  on  the  moon  cannot  be  used  in  building  an  irriga- 
tion dam  on  the  earth. 

Ill 


112  SOURCES  OF  EFFICIENCY 

Evidently  also  in  determining  whether  an  object  is  to  be  regarded 
as  auxiliary  much  depends  on  what  is  regarded  as  naturally  and 
inherently  a  part  of  any  given  object  or  domain.  This  is  a  matter 
to  be  considered  more  fully  later  (see  p.  123).  Meantime  it  is  well 
to  note  that  among  the  more  important  objects  which  are  often 
plainly  used  as  externality  agencies  of  efficiency  are  various  material 
objects;  in  particular  all  tools  and  machines,  and  various  physical 
forces;  plants  as  sources  of  clothing,  as  medicines,  and  in  other 
ways ;  animals  as  beasts  of  burden,  as  sources  of  clothing,  etc. ;  other 
persons,  ideas,  theories,  symbols,  efficiency  and  other  principles, 
categories  like  space  and  time;  or  complexes  of  these  objects. 

Many  important  individual  objects  which  belong  to  those  various 
classes  will  be  mentioned  in  the  pages  which  follow. 

Quantitative  Species  of  Externality 

It  is  also  important  to  classify  externalities  with  respect  to  the 
forms  which  they  may  assume. 

With  regard  to  the  categories  of  quantity  and  space,  an  externality 
may  be  large  or  small ;  near  or  remote ;  a  fringe,  a  background,  or  a 
betweenness ;  local,  superficial,  or  pervasive ;  and  of  various  geomet- 
ric shapes. 

It  is  also  important  to  remark  that  an  externality  may  be  of  one, 
two,  or  three  dimensions.  A  long  cable  is  said  to  be  the  life  of  a 
ship.  The  cable  in  this  case  may  be  regarded  as  a  linear  or  one- 
dimensional  externality.  A  three-dimensional  externality  is  em- 
ployed when  the  whole  of  a  mass  of  water  is  boiled  in  order  to  kill 
a  few  germs  contained  in  it,  or  when  practically  all  the  carbon  is 
expelled  from  iron  in  one  of  the  Bessemer  processes  of  making 
steel,  so  as  to  make  it  possible  to  introduce  exactly  the  right  per  cent 
afterward. 

An  externality  may  also  take  what  may  be  called  the  point  form. 
We  use  this,  for  instance,  when,  in  mastering  a  subject,  we  leap 
ahead  from  one  leading  point  to  another,  and  afterward  rapidly 
fill  in  the  intervening  gaps  or  let  them  fill  in  themselves.  A  similar 
instance  is  the  mastery  of  any  field  by  first  mastering  its  strategic 
points. 

The  importance  of  an  infinite  externality  is  illustrated  in  proofs 
by  exclusion  in  logic,  and  much  more  strikingly  by  the  value  of 
religious  ideas.  A  case  of  relatively  infinite  externality  is  that  of 
representing  zero  or  absence  of  number  by  the  symbol  o. 


EXTERNALITY 


113 


What  we  may  term  matrix  externality  is  often  expressed  by  the 
word  "environment". 

It  is  frequently  useful  to  characterize  an  externahty  by  means  of 
the  category  of  number.  Thus  an  externality  may  be  dual  in  the 
sense  that  it  is  composed  of  two  elements  as  when  both  water  and 
heat  are  used  in  preparing  food  by  the  method  of  boiling.  Similarly 
an  externality  may  be  triple  or  w-fold.  An  illustration  of  the  latter 
is  the  repeated  use  of  the  pendulum  in  determining  the  force  of 
gravity  at  a  given  place. 

Or  an  externality  may  be  manifold  in  the  sense  that  it  is  used  in 
many  ways,  or  by  many  persons  at  the  same  time,  as  when  a  railroad 
or  an  idea  is  used  by  many  persons  simultaneously. 

Temporal  Species  of  Externality 

A  case  of  externality  may  frequently  be  characterized  by  some 
category  of  time.  Thus  a  scaffolding  is  a  temporary  externality, 
while  the  finished  building  may  be  a  permanent  one.  When  time  is 
used  as  a  representative  of  what  is  contained  in  time,  an  externality 
involved  in  time  may  conveniently  be  spoken  of  as  temporal.  Ex- 
ternality of  this  kind  is  practiced  by  the  man  who  is  longheaded,  or 
forehanded,  or  patient.  Another  form  of  temporal  externality  is 
illustrated  by  the  manner  in  which  the  Rothschilds  in  London  learned 
of  the  results  of  the  battle  of  Waterloo  several  hours  before  any  one 
else  in  the  city  and  made  the  earlier  knowledge  the  source  of  finan- 
cial profit.  All  preventive  and  prophetic  work  is  full  of  the  extern- 
ality of  time.  Another  aspect  of  the  matter  is  expressed  by  the 
proverb  "All  things  come  to  him  who  waits". 

Still  another  case  of  temporal  externality  is  that  of  suspended 
operations  in  mathematics  in  order  ultimately  to  save  work  by 
cancellation  or  elimination  of  other  kinds.  The  same  mode  of 
obtaining  efficiency  applies  in  many  other  fields. 

The  result  aimed  at  in  any  process  also  constitutes  what  is  in  one 
respect  a  temporal  externality. 

Other  Important  Forms 

If  we  combine  the  idea  of  number  with  that  of  order  we  get 
the  idea  of  reciprocity  and  hence  of  reciprocal  externality.  Illus- 
trations of  this  are  the  two  blades  of  a  pair  of  scissors,  man  and 
wife,  mind  and  body,  algebra  and  geometry,  or  the  fruitful  interac- 
tion of  theory  and  practice  in  any  department  as  in  engineering. 


114  SOURCES  OF  EFFICIENCY 

Similarly  we  may  have  triple  or  w-fold  reciprocal  externality,  as 
that  existing  among  the  five  senses,  or  the  various  organs  of  the 
body,  the  members  of  a  family  or  community,  the  machines  in  a 
factory,  or  the  various  departments  of  knowledge  and  action,  as 
agriculture,  chemistry,  biology,  and  mining. 

An  important  special  case  is  what  is  called  the  comparative 
method  of  testing  a  principle  in  history  or  a  problem  in  science. 
Thus  an  important  way  of  getting  light  on  republican  government 
is  to  study  all  historic  republics  side  by  side. 

As  to  force  an  externality  may  be  reluctant  or  automatic.  Thus 
vision  is  characterized  by  certain  large  externalities  which  are 
automatic  and  irresistible,  as  well  as  by  others  which  are  voluntary. 
Motion  often  constitutes  an  efficient  externality  as  when  a  teacher 
enables  a  pupil  to  realize  certain  properties  of  a  cone  by  means  of 
the  rotation  of  a  right  triangle  generating  the  cone,  or  when  a 
teacher  unravels  any  complex  matter  by  causing  it  to  unfold  from 
certain  unit  principles. 

Various  adjectives  of  quality  may  be  applied  to  externalities. 
Among  the  most  important  are  the  terms  homogeneous  and  hetero- 
geneous. Thus  an  externality  may  be  homogeneous  (or  hetero- 
geneous) in  itself,  or  in  relation  to  the  material  to  which  it  is 
applied.  The  appliances  used  in  keeping  meat  by  cold  storage  are 
heterogeneous  in  both  of  the  above  respects.  An  important  case  of 
homogeneous  externality  is  that  of  doing  work  on  a  large  scale. 

An  extreme  case  of  heterogeneous  externality  is  that  which  may 
be  termed  negative  in  character.  In  this  species  the  datum  and  ex- 
ternality are  directly  opposite  in  nature  in  some  important  respect. 
Instances  are  a  difficulty  which  leads  to  new  discoveries  and  knowl- 
edge, or  a  defeat  or  a  misfortune  which  in  the  end  imparts  new 
power.  Of  like  nature  is  the  making  of  a  temporary  sacrifice  for 
the  sake  of  a  future  gain. 

In  relation  to  the  directive  faculty  in  man,  externalities  may  be 
classified  as  natural  or  artificial.  Thus  one  hand  is  a  natural  ex- 
ternality to  the  other.  Machines  and  buildings  are  examples  of 
artificial  externality.  The  results  of  a  mechanical  or  biological 
propagation  are  partly  natural  and  partly  artificial,  and  may  be 
termed  genetic  externality.  The  consequences  or  fruits  of  an  act 
or  principle  form  externalities  which  may  also  be  termed  genetic. 
In  many  cases,  externalities  of  this  last  kind  have  an  important  func- 
tion in  determining  the  essential  nature  of  an  act  or  lav^. 


EXTERNALITY  II5 

Important  cases  of  directive  externality  are  the  preparation  and 
use  of  reserves  of  any  kind  as  of  food,  water,  power,  money,  health, 
knowledge. 

With  respect  to  the  principle  of  limitation,  an  externality  may  be 
vague,  partial,  or  imperfect  in  any  way.  Thus  in  taking  an  oath  in 
court  use  is  made  of  infinite  externality,  but  usually  of  this  in  a 
very  obscure  and  general  form.  So  mystics  use  unlimited  exter- 
nality in  many  forms  all  of  which  are  more  or  less  difficult  to  under- 
stand. The  ether,  as  used  in  physics,  is  a  case  of  a  valuable  but 
imperfectly  understood  externality  in  the  field  of  science. 

It  is  often  an  advantage  to  combine  and  use  externalities  in  groups 
or  even  in  group  systems.  Thus  in  irrigating  a  large  piece  of  land  a 
group  of  auxiliaries  is  used  in  the  form  of  dam,  ditches,  pipes,  tools, 
men,  and  also  of  time,  ideas,  and  experience.  So  a  microscope 
(or  a  telescope),  and  the  various  facts  revealed  by  such  an  instru- 
ment form  a  group  of  related  externalities.  In  like  manner  if  we 
divide  a  set  of  externalities  into  two  groups,  viz. :  natural  and  arti- 
ficial, and  subdivide  each  of  these  groups  according  to  various 
spatial,  numerical,  temporal,  and  other  categories,  we  arrive  at  a 
multiplicative  group  system  of  externalities. 

Similarly  an  externality  may  be  of  high  or  low  order.  As  an 
example  of  a  dual  series  of  externalities  we  have  the  saying  "The 
pen  is  mightier  than  the  sword".  Space  and  time  are  auxiliaries  of 
a  higher  order  than  material  objects.  The  order  of  excellence  of 
an  externality  may  be  determined  in  various  ways,  as  by  the  number 
of  sub-externalities  included  in  the  given  externality,  or  by  its 
dimensions,  or  by  its  general  efficiency  power.  What  is  often  called 
"the  ideal"  in  any  department,  even  though  it  may  be  unattainable, 
often  constitutes  a  powerful  and  stimulating  externality. 

Complex  Externalities 

Evidently  the  different  species  of  externality  may  be  compounded 
and  complexed  in  many  ways.  Instances  of  such  complex  exter- 
nalities are  the  aggregate  of  externalities  found  in  a  large  factory, 
or  those  used  in  connection  with  courts  of  justice  in  the  punishment 
of  crime  or  the  settlement  of  disputes.  Vastly  more  extensive  and 
complex  is  the  combination  of  externalities  which  are  in  operation 
at  each  stage  of  human  progress. 


Il6  SOURCES  OF  EFFICIENCY 

EFFICIENCY    FUNCTIONS    OF    EXTERNALITY 

In  Studying  the  advantages  which  accompany  the  use  of  external- 
ity, it  is  evident  at  the  outset  that  an  extension  of  material  and 
methods  in  any  process  means  additional  opportunities  for  the  for- 
mation of  various  species  of  groups  and  for  reaping  the  efficiencies 
which  come  from  the  use  of  groups. 

Externality  leads  to  Reuse 

Lx)oking  at  the  matter  in  more  detail,  externality  opens  the  way 
to  important  cases  of  reuse.  For  instance  the  application  of  paint 
to  a  wooden  house  keeps  the  material  of  the  house  from  rotting 
and  thus  prolongs  the  use  of  the  house.  It  is  to  be  noted  also  that 
the  house  itself  is  an  externality  which  prolongs  the  use  of  its 
contents.  So  the  immersion  of  a  biological  specimen  in  alcohol 
leads  to  the  preservation  and  repeated  use  of  the  specimen. 

The  combination  of  many  business  establishments  into  one  is 
frequently  followed  by  the  reuse  by  all  the  rest  of  what  is  best  in 
each  one  of  the  constituent  businesses. 

Externality  also  leads  to  more  abstract  and  general  forms  of 
reuse.  Thus  by  showing  that  two  objects  are  each  equal  to  a  third 
object,  we  may  show  that  they  are  equal  to  each  other.  The  third 
object  in  this  case  may  be  regarded  as  an  externality  the  employ- 
ment of  which  saves  the  labor  of  an  often  difficult  direct  comparison 
of  the  two  original  objects.  The  extended  use  of  this  principle 
leads  to  the  method  of  measurement  in  dealing  with  objects  and  to 
all  the  fruits  of  measurement. 

Taking  a  wide  view  of  things  or  doing  things  on  a  large  scale 
frequently  opens  the  way  to  numerous  economies  and  efficiencies 
among  the  most  important  of  which  is  prophetic  reuse.  For  ex- 
ample the  U.  S.  Weather  Bureau  in  the  year  1903  observed  tor- 
rential rains  on  the  Upper  Missouri  River  and  predicted  a  flood  on 
the  Mississippi  28  days  before  it  arrived  at  certain  places  and  thus 
saved  many  millions  of  dollars.  The  same  bureau  has  diminished 
the  annual  loss  to  shipping  on  the  Great  Lakes  by  fifty  per  cent. 

Leads  to  Multiplicative  Results 

The  externality  of  outflanking  an  enemy  opens  the  way  to  the 
multiplicative  effect  of  an  enfilading  fire.  In  a  much  more  general 
way  the  consideration  of  a  large  domain  of  material  gives  oppor- 


EXTERNALITY  II7 

tunity  for  the  discovery  or  invention  of  units  and  multipliers  of 
unusual  excellence. 

Economies 

The  use  of  auxiliary  instruments  results  in  a  vast  variety  of 
economies  as  of  strength,  time,  space,  and  resources  of  all  kinds. 
At  one  time  it  took  78  men  i^  minutes  to  put  over  the  helm  of  a 
large  vessel;  later  by  the  aid  of  steam,  the  work  was  done  by  2  men 
in  16  seconds.    Every  field  of  activity  contains  similar  illustrations. 

New  Groups  and  Group  Systems 

General  externality  and  special  auxiliary  objects  are  alike  potent 
aids  in  the  formation  of  groups  and  of  group  systems.  A  simple 
instance  is  the  formation  of  a  bundle  by  tying  objects  together  with 
twine.  The  use  of  a  club,  or  of  a  bow  and  arrow,  gave  the  savage 
concentration  of  his  strength  both  in  time  and  space.  The  use  of 
the  gun  and  bullet  does  the  same  in  a  far  greater  degree.  The 
externality  of  a  copper  wire  on  a  railroad  leads  to  the  concentration 
of  many  locomotives  into  one  central  power  engine. 

So  the  use  of  a  clock  gives  us  an  accurate  and  detailed  multi- 
plicative grouping  of  time.  In  a  far  larger  way  the  telegraph,  tele- 
phone, and  various  similar  appliances  of  modern  life  make  the  world 
one  large  group,  and  also  a  system  of  groups  in  many  ways.  With 
reference  to  a  special  field  like  that  of  books,  it  has  been  remarked 
that  the  ''literature  which  enlarges  the  outlook,  also  transforms  the 
mind".  Or,  as  Thoreau  says,  "Only  that  intellect  makes  any  pro- 
gress toward  conceiving  the  essence  of  a  matter  which  at  the  same 
time  perceives  its  effluence." 

Accuracies  and  Delicacies 

Externality  frequently  produces  those  uniformities  and  accuracies 
which  are  the  source  of  much  efficiency  (see  Chapter  VIII,  p.  130). 
Examples  are  the  continuity  of  action  obtained  by  the  use  of  a  fly- 
wheel or  a  reserve  of  any  kind,  stability  acquired  by  aid  of  ballast 
or  a  bilge  keel,  or  accuracy  by  aid  of  extra  tests  or  apparatus. 

In  like  manner  auxiliary  appliances  are  often  a  source  of  useful 
diversity,  fluidity,  or  sensitiveness.  A  simple  instance  is  that  of 
making  food  tender  by  the  use  of  heat.  By  the  aid  of  the  bolometer 
a  difference  of  temperature  of  less  than  .0001  °  may  be  detected.    In 


Il8  SOURCES  OF  EFFICIENCY 

making  glass  the  addition  of  soda  lowers  the  melting  point  of  sand 
from  3000°  to  2400°,  and  lime  is  useful  in  the  same  way  in  reducing 
iron  ore.  By  using  the  proper  apparatus  several  thousand  successive 
photographs  of  a  moving  object  may  be  taken  in  one  minute  and 
the  action  of  the  corpuscles  of  the  blood,  for  instance,  traced  in 
detail. 

A  Source  of  Orders  of  Materials 

Similarly  the  use  of  an  externality  is  often  a  means  of  obtaining 
a  useful  multipHcative  gradation.  Thus  if  two  tracks  are  used  on 
a  railroad  in  a  given  direction  one  can  be  used  for  fast  trains  and 
the  other  for  slow  trains  with  many  resultant  advantages. 

Some  one  has  said  that  to  get  down  to  the  pith  of  a  matter  one 
must  go  round  the  matter  and  study  it  in  all  its  bearings.  Ex- 
pressed in  other  words  this  means  that  a  varied  externality  is  neces- 
sary in  discovering  the  causes,  sources,  and  essential  efficientism  in 
any  domain.  Thus  a  consideration  of  the  needs,  rights,  and  op- 
portunities of  all  classes  of  men  leads  to  a  multiplicative  series  of 
ethical  principles  capped  by  what  is  at  least  an  approximate  or 
efficiency  absolute  represented  perhaps  by  a  sense  of  oughtness  01 
Kant's  categorical  imperative. 

Thus  also  the  combination  at  Jerusalem  as  at  a  focus,  of  the 
various  externalities  represented  by  Egyptian,  Assyrian,  Persian, 
Greek,  and  Roman  civilizations  was  instrumental  in  leading  to  the 
development  at  that  place  of  the  Jewish  and  Christian  religions. 
In  any  field  of  work  breadth  of  view  as  to  ends  aimed  at  is  import- 
ant in  obtaining  efficiency  of  a  high  order.  Efficiency  for  selfish 
ends  is  not  efficiency  at  all  in  the  long  run. 

New  Powers  of  Management 

A  broad  view  of  things  is  also  a  source  of  efficiency  in  that  it 
leads  to  a  higher  and  more  effective  use  of  man's  directive  powers 
(see  Chapter  XI,  p.  192),  and  is  productive  of  many  valuable  utili- 
zations and  substitutions.  It  gives  a  wider  range  of  material  to 
select  from,  more  space  in  which  to  act,  and  many  aids  in  transfer- 
ring objects  in  space.  Thus  a  lampshade  enables  us  to  direct  light 
to  a  place  of  need  and  thus  more  fully  to  utilize  the  light.  By  the 
use  of  salt,  vinegar,  tin,  or  cold  storage,  we  can  preserve  food  and 
direct  its  use  with  respect  to  the  categories  of  both  time  and  place. 


EXTERNALITY  II9 

Externality  is  often  a  source  of  efficiency  by  enabling  us  to  sub- 
stitute a  material  or  force  that  costs  little  for  that  which  costs 
much,  as  in  the  use  of  water-power  instead  of  hand-power  to  saw 
lumber. 

Externality  also  assists  in  getting  results  by  enabling  us  to  apply 
energies  and  resources  at  important  centers.  Thus  Napoleon  by 
taking  a  large  view  of  the  field  of  operations  was  able  to  strike  the 
enemy  in  the  rear  at  Marengo  and  thus  to  win  the  campaign  by  a 
single  battle.  So  in  general  a  large  view  of  matters  reveals  centers 
of  influence  and  also  the  means  of  reaching  and  mastering  these, 
centers  and  thus  obtaining  multiplicative  results. 

Prevention  of  Loss 

The  use  of  externality  often  produces  important  results  in  what 
is  at  first  a  negative  form.  Thus  a  broad  view  of  a  given  matter 
may  prevent  error,  sickness,  or  even  loss  of  life.  The  use  of  an 
arbiter  to  settle  a  dispute  renders  prejudice  inoperative.  The 
breadth  of  view  gained  by  education  and  travel  is  a  safeguard 
against  hasty  generalizations,  or  overuse  of  any  one  method.  A 
somewhat  similar  qualitative  result  springing  from  the  use  of  ex- 
ternality is  the  conversion  of  an  obstacle  into  a  stepping  stone,  or 
of  a  defeat  into  a  victory. 

Unique  Fruits 

Some  of  the  results  obtained  by  the  use  of  externality  are  unique 
or  transcendental  in  the  sense  that  apparently  they  could  not  have 
been  obtained  without  the  use  of  this  principle  in  some  form.  Thus 
the  aeroplane  enables  a  man  to  fly.  The  yellow  fever  parasite  is  so 
small  as  to  be  invisible  in  the  microscope  yet  it  can  be  entirely  con- 
trolled by  indirect  means.  The  same  is  true  of  the  germs  of  several 
other  diseases,  as  rinderpest,  and  pellagra.  By  the  use  of  the 
Roentgen  rays  the  action  of  the  heart  and  lungs  may  be  seen  and 
photographed.  By  the  same  means  when  bismuth  salts  have  been 
added  to  the  food  the  progress  of  this  food  during  the  whole  process 
of  digestion  may  be  watched.  Religious  conversions  as  produced 
by  the  action  of  infinite  externality  upon  the  individual  form  an 
illustration  of  beneficial  results  of  an  incomparably  higher  type. 


120  SOURCES  OF  EFFICIENCY 

Complex  Fruitages 

It  is  scarcely  necessary  to  add  in  this  connection  that  the  above 
classes  of  efficiency  functions  may  be  compounded  and  complexed 
in  an  endless  variety  of  ways.  For  instance  externality  in  the  form 
of  an  anticipation  of  future  rewards  often  begets  various  efficiency 
advantages.  Such  an  anticipation,  for  example,  arouses  a  feeling 
of  joy  in  the  worker  which  increases  his  efficiency  in  a  number  of 
ways  as  by  stimulating  his  various  activities,  increasing  his  speed, 
causing  him  to  search  for  new  knowledge,  and  perhaps  leading  hirri 
to  invent  new  methods. 

Greater  Use  of  Externality  in  Higher  Organisms 

If  we  wish  to  look  at  the  fruits  of  externality  in  a  more  collective 
and  pictorial  way  we  find,  for  instance,  that  the  higher  we  go  in  the 
scale  of  organisms  the  greater  is  the  use  of  auxiliaries.  The  spider 
has  its  web,  and  the  bird  its  nest,  but  man  has  his  cities,  railroads 
and  philosophies. 

If  we  examine  the  various  definitions  which  have  been  made  of 
man  for  the  purpose  of  discriminating  between  him  and  the  lower 
animals,  we  find  that  the  essential  part  of  each  of  these  statements 
is  the  conception  of  man  as  an  animal  using  externality  in  some 
explicit  and  conscious  way.  Thus  man  has  been  defined  as  the  tool 
using  animal;  as  an  animal  looking  before  and  behind;  the  cause 
using  animal  (das  ursachen  Thier)  ;  a  rational  animal;  the  animal 
requiring  the  superfluous. 

Greater  Use  by  Greater  Men 

Furthermore  it  is  to  be  noted  that  the  greatest  men  are  those  who 
have  used  the  most  and  highest  externality.  A  study  of  great  men 
in  the  schoolboy  stage  has  shown  that  their  most  common  charac- 
teristic is  a  tendency  to  break  out  of  ruts  and  discard  conventions. 
The  use  of  this  and  other  forms  of  externality  increases  as  they 
develop. 

Time  and  tide,  it  is  said,  are  always  on  the  side  of  great  men. 
As  a  matter  of  fact  such  men  have  such  an  outside  and  comprehen- 
sive vision  of  affairs  that  they  are  enabled  to  utilize  time  and  tide 
for  their  own  purposes. 


EXTERNALITY  121 

:Human  Progress  Marked  by  an  Increasing  Use  of  Externality 

Hence  it  is  not  surprising  that  each  stage  of  human  progress  has 
been  marked  by  an  increasing  use  of  externality  in  its  various  forms. 
The  first  club  or  stone  used  thus  has  developed  into  the  present 
mighty  volume  of  machinery  of  all  kinds,  material,  linguistic,  social, 
artistic  and  logical. 

Furthermore  an  examination  of  each  department  of  activity  and 
of  each  element  of  civilization  reveals  the  same  law  of  increasing 
auxiliaries.  Thus  the  knowledge  required  of  the  expert  agricul- 
turist has  increased  till  at  the  present  time  he  must  use  the 
main  principles  and  some  of  the  details  of  chemistry,  physics, 
botany,  biology,  engineering,  meteorology,  commerce,  and  social 
psychology. 

Lack  of  Externality  Means  Loss 

x\nother  method  of  gaining  an  appreciation  of  the  importance  of 
externality  is  to  try  to  picture  what  life  would  be  without  certain 
of  the  auxiliary  instrumentalities  now  in  common  use.  If,  for 
instance,  in  navigation  we  take  away  steam  and  gas  we  reduce 
transportation  by  water  to  the  use  of  sail  vessels;  if  we  take 
away  masts  and  sails,  we  have  left  boats  propelled  by  oars ;  if  we 
remove  wood  and  skins,  man  must  propel  himself  in  the  water  by 
swimming. 

One  reason  why  man  has  not  been  able  to  analyze  the  force  of 
gravitation  into  constituent  elements  is  that  this  force  is  so  perva- 
sive that  it  has  thus  far  been  impossible  to  get  an  outside  point  from 
which  to  view  it;  that  is,  it  has  been  impossible  to  apply  any  compre- 
hensive externality  to  it. 

Likewise  in  the  higher  mental  world,  the  man  without  externality 
is  the  narrow,  selfish,  and  therefore  blighted  man. 

Familiar  Words  Showing  the  Value  of  Externality 

Still  another  way  of  obtaining  an  insight  into  the  power  of  ex- 
ternality is  to  recall  the  efficiencies  connected  with  words  or  phrases 
which  denote  certain  more  or  less  familiar  forms  of  externality, 
such  for  instance  as  tools,  machinery,  breadth  of  mind,  reserves, 
:Solidarity,  outwit,  undermine,  correlations,  larger  horizon. 


122  SOURCES  OF  EFFICIENCY 

Limitations  in  the  Utilities  of  Externality 

Finally  in  this  relation  mention  should  be  made  of  the  limitations 
and  often  drawbacks  connected  with  externality  as  a  source  of  effi- 
ciency. Externality,  of  necessity,  means  an  added  amount  of  ma- 
chinery to  carry  and  often  the  annexed  toolage  does  not  pay  for 
itself.  It  then  becomes  mere  red  tape  or  worse.  Too  much  light 
makes  a  confusing  glare  or  even  produces  blindness.  Wealth  with- 
out some  higher  externality  often  becomes  a  curse.  At  times  a. 
doubt  has  been  expressed  whether  modern  machinery  as  used  thus 
far  has,  on  the  whole,  improved  the  condition  of  mankind.  At 
least  we  can  say  the  burden  of  material  mechanism  carried  by 
modern  civilization  is  as  great  as  it  can  bear.  Another  class  of 
danger  connected  with  the  use  of  outside  auxiliaries  is  the  dwarfing^ 
of  one's  powers  of  self  reliance.  Other  aspects  of  this  evil  are 
expressed  by  the  proverb  "Too  many  cooks  spoil  the  broth",  and 
"What  is  everybody's  business  is  nobody's  business".  In  case  an 
externality  results  in  a  more  extended  multiplicative  group  system, 
the  drawbacks  presented  in  a  preceding  chapter  connected  with 
such  systems  will  also  be  present. 

It  is  well  to  note  also  that  the  dangers  connected  with  an  extern- 
ality often  correspond  in  size  to  the  useful  power  of  the  externality. 
The  efficiency  possibilities  of  unlimited  externality  for  instance  in 
the  best  religious  concepts  seem  to  be  boundless  yet  in  many  ways 
the  strength  of  religion  has  proved  to  be  its  weakness.  Seemingly 
as  a  consequence  of  the  prodigious  values  in  religion  have  come 
pride,  reluctance  to  use  other  sources  of  efficiency,  hostility  to  gen- 
eral culture,  cruelty,  and  general  persecution.  Hence  it  has  been 
said,  "The  vision  of  a  spiritual  ideal  is  the  most  important  single 
element  of  efficiency,  but  one  of  the  most  dangerous". 

Self-corrective  Power  in  Externality 

It  should  be  observed,  however,  that  externality  contains  within 
itself  the  power  largely  to  correct  its  own  defects  and  evils.  For  the 
high  order  of  multiplicative  power  which  results  from  such  extern- 
ality also  means  in  large  degree  the  power  of  self -correction  and 
sel  f -development. 

ANALYSIS 

In  order  to  get  a  more  precise  idea  of  the  nature  of  externality 
and  hence  to  increase  the  advantages  in  its  use,  we  shall  now  make 


EXTERNALITY 


123 


a  more  thorough  examination  of  the  elements  which  enter  into  it 
than  was  made  in  the  opening  paragraphs  of  the  chapter. 

Space  and  Like  Elements 

A  spatial  element  seems  necessary  to  the  idea  of  externality.  For 
the  term  implies  outsideness  to  what  is  given  or  customary,  and  the 
concept  of  something  outside  or  beyond  is  a  spatial  one. 

It  is  to  be  noted,  however,  that  in  the  more  abstract  forms  of 
externality  the  idea  of  space  is  refined  till  in  some  respects  this  idea 
seems  to  disappear  altogether.  An  instance  in  point  is  the  use  of 
an  abstract  quality  or  method  of  some  kind  as  an  auxiliary.  Physi- 
cally a  quality  may  be  as  innerness,  while  in  the  domain  of  mental 
attention  it  is  outside  of  what  was  included  in  the  consciousness  of 
the  doer  at  the  start. 

The  element  of  time  is  also  present  to  some  extent  in  externality. 
For,  at  least  with  respect  to  the  conscious  apprehension  of  them,  the 
auxiliary  used  follows  that  which  was  first  tried  without  the  ex- 
ternality, and  hence  we  have  in  each  use  of  externality  some  flavor 
of  succession  or  order. 

The  element  of  mind  or  consciousness  is  also  usually  present, 
since  the  use  of  something  beyond  what  is  customary  implies  a 
certain  element  of  effort  or  surprise.  Looked  at  in  another  way, 
externality  implies  first  an  enlargement  of  the  mind  and  then  of  the 
material  used  or  considered. 

The  meaning  of  externality  may  also  be  expressed  in  terms  of  the 
group.  From  this  point  of  view  externality  means  an  enlarged 
group,  the  result  being  obtained  by  removing  some  limitation  in 
the  datum  group. 

Relativity  of  Externality 

From  the  preceding  discussion  it  is  evident  that  the  element  of 
relativity  is  prominent  in  determining  whether  a  given  object  or 
process  is  a  case  of  externality  or  not.  What  is  externality  from 
one  point  of  view  may  not  be  so  from  another.  To  the  savage  chief 
the  use  of  a  messenger  would  be  natural  and  the  use  of  mails  an 
externality,  while  to  a  modern  business  man  who  has  come  to  regard 
the  use  of  the  mails  as  natural,  the  use  of  a  special  messenger  would 
usually  seem  an  externality.  Similarly  the  use  of  salt  in  one's  food, 
or  of  medicine,  or  of  clothing,  may  or  may  not  constitute  an  extern- 
ality according  to  circumstances. 


124  SOURCES  OF  EFFICIENCY 

The  two  extreme  points  of  view,  in  this  respect,  with  regard  to 
externality  should  here  be  stated.  Thus  from  the  point  of  view  of  a 
single  monad,  the  rest  of  the  universe  is  an  externality.  But  from 
the  universal  point  of  view,  there  is  no  such  thing  as  externality, 
but  all  efficiency  is  an  internal  process  in  the  universe  as  a  whole. 
These  extreme  conceptions  are  useful  since  they  are  themselves, 
with  respect  to  the  customary  use  of  this  agent,  special  cases  of 
externality.  However,  under  usual  conditions  it  is  an  advantage  to 
divide  a  situation  into  what  is  ordinary  and  what  is  extraordinary 
or  external  to  the  ordinary. 

It  is  also  well  to  remember  that  in  externality  as  well  as  in  each 
of  the  other  Efficients  there  is  a  characteristic  or  unique  element^ 
something  perhaps  beyond  analysis. 

Auxiliaries  vs.  Externality 

It  may  also  be  well  in  this  connection  to  point  out  the  essential 
difference  between  the  terms  auxiliaries  and  externality.  Auxiliar- 
ies are  usually  subordinate  in  size  and  importance  to  the  main 
datum  or  method  while  an  externality  may  be  superior  to  the  datum 
and  may  dominate  it.  The  term  auxiliaries  also  implies  a  more 
direct  and  immediate  use  than  does  externality. 

In  conclusion  we  have  the  following  approximate  definition: 

Externality  is  a  method  of  obtaining  results  by  the  application  of 
something  outside  of  the  customary  data. 

Also  the  outside  object  thus  used  is  often  termed  an  externality. 

METHODS  OF  APPLICATION 

Externality  as  a  Group 

Viewing  externality  as  a  larger  group,  and  hence  as  essentially  a 
higher  use  of  the  multiplicative  principle,  is  an  aid  to  the  efficient 
use  of  externality  in  several  ways.  For  it  leads  to  an  extended  use 
of  this  instrument  by  making  evident  the  great  value  of  this  method 
of  work,  by  revealing  the  vast  number  of  available  auxiliary  ob- 
jects, and  by  putting  such  objects  in  an  effective  form. 

Adaptation  in  its  Application 

Taking  up  the  matter  in  more  detail,  externality  is  so  broad  a 
principle  that  in  its  use,  relativity,  or  special  adaptation  in  peculiar 
cases,  needs  to  be  studied  carefully. 


EXTERNALITY  125 

In  many  situations  of  great  difficulty,  rather  than  to  use  no  extern- 
ality, it  is  well  to  use  the  principle  in  some  crude  form.  This  may 
be  a  blind  kind  of  externality  like  patience,  or  an  unformed  kind 
like  agitation,  or  publicity,  or  the  mere  recording  of  facts  while 
waiting  for  laws  to  appear.  Compromise  is  often  a  complex  form 
of  crude  externality  since  in  it  patience  is  exercised  and  results  from 
two  or  more  simultaneous  series  of  developments  are  awaited. 

Externality  by  Doubling 

A  simple  but  widely  applicable  form  of  externality  is  that  which 
consists  of  doubling  a  given  object  or  repeating  a  given  process. 
Nature  has  employed  this  source  of  efficiency  in  giving  man  two 
hands  and  two  eyes.  Man  utilizes  the  same  method  when  he  in- 
stalls two  engines  in  a  power  house,  or  checks  the  result  obtained 
from  a  computation  by  repeating  the  calculation. 

Preference  to  Highly  Developed  Externalities 

In  using  externalities  it  is  evidently  important  to  learn  to  recog- 
nize those  auxiliaries  which  are  highly  developed  and  therefore 
unusually  effective  and  to  give  the  preference  to  such  species.  In 
this  connection  it  is  to  be  noted  that  a  high  externality  is  usually 
more  or  less  abstract,  and,  for  our  purpose,  closely  related  to  the 
Efficients.  It  has  also  in  many  cases  acquired  a  tendency  to  act, 
so  to  speak,  of  itself. 

Even  when  an  additive  externality  would  answer  a  given  purpose 
it  is  often  well  to  use  a  highly  multiplicative  process  giving  larger 
results  than  are  needed  and  to  apply  the  extra  results  to  the  apices 
of  some  other  group  system. 

A  small  or  superficial  externality  is  often  dangerous  but  one 
cannot  possess  too  much  externality  in  its  higher  forms.  One 
reason  for  this  is  that  the  higher  forms  carry  with  them  in  an 
unusual  degree  their  own  corrective,  as  well  as  more  aggressive  prin- 
ciples of  development. 

Educational  Sources  of  Externality  Powers 

In  the  process  of  acquiring  externality  powers  it  is  well  to  remem- 
ber that  the  study  of  a  certain  subject  or  some  special  form  of 
experience  is  often  particularly  fitted  to  give  mastery  of  some 
special  kind  of  externality.    Thus  geography  gives  a  grasp  of  space. 


126  SOURCES  OF  EFFICIENCY 

geology  of  time,  astronomy  of  space  and  time,  chemistry  of  quality, 
physics  of  force,  psychology  of  mind,  and  history  of  time  and 
mind. 

The  effective  application  of  the  principle  of  externality  is  also 
often  greatly  aided  by  the  use  of  certain  of  the  primal  sources  of 
efficiency  to  be  studied  in  the  chapters  which  follow.  Thus  the 
analysis  (see  Chapter  VIII)  of  a  domain  into  different  well  se- 
lected elements  often  opens  the  way  to  obtaining  important  extern- 
alities by  a  mere  extension  of  certain  of  these  elements.  Also 
appropriate  symbols  (see  Chapter  X)  are  an  aid  in  grasping  large 
externalities  and  in  applying  them.  The  use  of  symbols,  for  in- 
stance, may  lead  to  standard  methods  of  transforming  and  adapting 
auxiliaries  and  obtaining  results  from  them  by  semi-mechanical 
means. 

Ideal  Species 

It  is  ever  to  be  borne  in  mind  that  for  our  purpose  the  most  im- 
portant externality  is  that  of  the  aggregate  of  the  Efficients  com- 
bined in  the  most  effective  way  and  kept  ready  for  use  at  any 
moment.  It  is  to  be  noted  also  that  each  individual  person  may 
advantageously  develop  this  general  form  into  a  special  form  or 
shape  adapted  to  his  peculiar  circumstances.  It  will  also  be  recog- 
nized that  the  use  of  the  above  ideal  constitutes  a  use  of  externality 
of  externality. 

Synopsis  of  Chapter 

The  principal  results  arrived  at  in  this  chapter  are  as  follows. 
Not  only  may  the  organization  of  given  material  produce  efficiency 
in  its  use,  but  an  equal  or  even  greater  increase  of  efficiency  may 
often  be  obtained  by  going  outside  of  the  given  situation  and  ap- 
plying certain  auxiliaries  to  the  data  in  hand.  Evidently  the  use 
of  outside  material  may  be  of  innumerable  kinds  since  it  may  in- 
clude an  endless  variety  both  of  objects  and  also  of  the  forms  in 
which  these  objects  may  be  assembled  or  viewed. 

The  fundamental  source  of  new  power  in  externality  is  that  it, 
from  its  very  nature,  opens  the  way  to  the  formation  of  new  and 
larger  groups,  and  hence  means  larger  and  higher  forms  of  reuse, 
multipliers,  groups,  and  group  systems,  with  the  various  consequent 
fruitages  of  each  of  these.     Of  particular  importance  are  the  new 


EXTERNALITY  127 

possibilities  of  directive  management  which  arise.  Many  valuable 
results  otherwise  impossible  are  also  obtained.  Hence  human 
progress  has  ever  been  marked  by  an  increased  use  of  externality  of 
various  kinds. 

So  powerful  is  this  source  of  efficiency,  that  it  is  especially  im- 
portant to  realize  the  great  number  of  forms  which  it  assumes,  and 
the  frequently  large  value  of  even  its  crudest  and  most  elementary 
species.  At  the  same  time  the  greatest  stress  should  be  laid  on  its 
highest  forms,  and  careful  study  be  made  of  the  sources  from 
which  these  may  be  obtained. 


EXERCISE  7 

State  the  class  or  classes  to  which  each  of  the  following  externalities 
belongs : 

1.  An  axe  4.  Darkness  as  a  revealer  of  stars 

2.  Sunlight  5.  A  relay  circuit  on  a  telegraph  line 

3.  Business  capital  6.  A  name 

7.  Heat  used  to  expand  a  wagon  tire  before  placing  the  tire  on  the  rim 
of  the   wheel. 

8.  Heat  used  in  making  ice. 

9.  A  line  added  to  a  diagram  to  aid  in  proving  a  proposition  in  geometry. 
ID.  The   third    dimension   of    space,    as    utilized   by   a    man    riding   in    an 

aeroplane. 

11.  An   ambuscade. 

12.  Boiling  water  to  kill  the  germs  in  it. 

13.  During  the  blizzard  of  the  year  1888,  a  telegram  was  sent  from  New 
York  to  Boston  by  the  way  of  Paris.  What  externalities  were  employed 
in   this   process? 

14.  Give  an  example  of  each  of  the  principal  kinds  of  externality. 
State  the  principal  kinds  of  externality 

15.  Gained  by  travel. 

16.  Afforded  by  an  education  in  the  ordinary  sense  of  the  term. 

17.  Used  by  an  intelligent   farmer. 

18.  By  a  teacher. 

19.  Employed  in  the  manufacture  of  pottery. 

20.  In  mining  coal. 

21.  State  the  different  kinds  of  externality  involved  in  mental  conscious- 
ness. 

22.  Which  of  the  mental  powers  (as  memory,  etc.)  supply  noteworthy 
externalities? 

23.  What  externalities  are  used  in  writing  a  letter  and  sending  it  by  mail? 

24.  Explain  altruism  as  a  form  of  externality  and  the  efficiencies  which 
result. 


128  SOURCES  OF  EFFICIENCY 

25.  Give  three  instances  of  the  use  of  color  as  an  externaHty. 

26.  Also  of  the  use  of  heat  in  this  way. 

27.  Also  of  water. 

28.  State  the  kinds  of  externality  used  by  an  ordinary  bird. 

29.  In  a  certain  factory  1000  yards  of  a  given  kind  of  cloth  can  be  manu- 
factured at  a  cost  of  $800,  and  50,000  yards  at  a  cost  of  $32,000.  The 
efficiency  of  the  first  process  is  what  per  cent  of  that  of  th;  second?  What 
externalities  are  here  the  source  of  efficiency? 

30.  Before  the  use  of  power  machinery  in  making  muslin,  1000  operators 
could  produce  10,000  yards  in  a  certain  time.  After  the  introduction  of 
such  machinery  50,000  operatives  in  the  same  time  produced  4,000,000  yards. 
Express  the  degree  of  human  efficiency  here  involved.  What  externaHties 
were  the  source  of  this  efficiency? 

31.  By  direct  computation  obtain,  to  three   decimal  places,  the  numerical 

value  of-y==:.  Also  compute  this  value  after  first  rationalizing  the  denom- 
inator of  the  given  fraction.  State  the  degree  of  labor  efficiency  involved. 
What  externality  is  used  in  obtaining  this  efficiency? 

32.  If  a  man  without  a  machine  can  plant  i  acre  of  potatoes  in  i  day, 
while  a  man  with  a  machine  can  plant  zVz  acres,  state  the  degree  of  human 
efficiency  in  the  second  process  and  the  source  of  the  same. 

2,2,-  Of  what  advantage  is  it  to  a  boxer*  to  keep  in  more  or  less  constant 
motion  ? 

34.  State  the  advantages  in  the  use  of  a  large  storage  battery  in  connec- 
tion with  a  city  electric  railway. 

35.  State   the   difference  between   parsimony  and   economy. 

36.  Point  out  the  advantages  in  using  a  somewhat  larger  furnace  than 
is  actually  required  in  heating  a  house. 

37.  Also  in  the  use  of  a  fountain  pen  as  compared  with  an  ordinary  pen. 

38.  State  as  fully  as  you  can  the  externalities  now  used  by  physicians 
which  were  not  used  by  them  one  hundred  years  ago. 

39.  What  kinds  of  externality  are  involved  in  publicity  as  to  governmental 
affairs,  and  what  are  the  advantages   which   result? 

40.  Give  an  example  where  the  use  of  externality  results  in  a  loss  of 
efficiency. 

41.  Show  that  reuse  always  implies  externality. 

42.  Give  three  examples  of  groups  formed  by  the  use  of  externality. 

43.  What  kinds  of  externality  did  Vergil  use  when  he  wrote  many  lines 
in  the  morning  and  cut  them  down  to  a  few  by  evening,  and  what  were 
the    advantages   involved  ? 

44.  Give  an  instance  where  the  use  of  crude  externality  rather  than  of 
none  is  advantageous. 

45.  Instead  of  telephoning  a  given  message  it  is  sometimes  more  advan- 
tageous to  send  the  message  in  a  written   form.     Why? 

46.  What  are  the  advantages  to  a  business  man  in  keeping  a  considerable 
cash  reserve  on  hand? 

47.  In   carrying  on   commerce   with   another  country    (especially   one   low 


EXTERNALITY 


129 


in  the  scale  of  civilization)  it  has  been  found  useful  to  learn  the  history, 
geography,  and  customs  of  the  country.  What  externalities  and  resulting 
advantages  are  involved  in  this  procedure? 

48.  State  the  externality  involved  in  realizing  the  future  rewards  of  pres- 
ent work  and  the  advantages  of  such  realization.  State  also  some  efficient 
ways  of  making  such  externality  vivid  to  different  classes  of  people,  as  to 
pupils,   or  workmen. 

49.  What  advantages  result  from  reasoning  a  principle  out  to  its  logical 
consequences  before  applying  it?  What  forms  of  externality  are  here: 
involved  ? 


CHAPTER  VIII 

UNIFORMITY   AND   DIVERSITY 

Illustrations  of  Diversity  as  a  Source  of  Efficiency 

The  separation  of  an  object  into  parts  with  a  view  to  the  in- 
dividual treatment  of  these  parts  is  often  a  fundamental  source  of 
efficiency.  Watt's  invention  of  a  separate  condenser  changed  the 
steam  engine  from  a  toy  to  the  most  effective  machine  in  man's 
possession.  Flight  by  the  aeroplane  was  made  a  practical  success  by 
dividing  the  wings  of  the  machine  into  parts  so  that  they  could  be 
warped  with  such  exactness  as  to  make  stability  possible  amid 
shifting  air  currents.  The  triumphs  of  modern  surgery  come  from 
regarding  the  human  body  not  as  a  lumpish  whole  but  as  made  up 
of  separate  cells,  and  also  from  keeping  the  germs  of  infection 
away  from  wounds. 

The  source  of  efficiency  thus  illustrated,  we  term  diversity.  More 
complex  and  abstract  examples  of  its  value  are  the  beneficial  results 
arising  from  the  separation  of  church  and  state,  from  individual 
ownership  of  property,  and  from  the  distinction  between  what  is 
personal  and  impersonal. 

Illustrations  of  Uniformity  as  a  Source  of  Efficiency 

In  like  manner,  and  often  in  a  closely  related  way  the  principle  of 
uniformity  or  sameness  is  a  highly  important  aid  in  obtaining  use- 
ful results.  Thus  the  fact  that  the  same  units  of  money  are  used 
in  all  parts  of  a  given  country  saves  the  traveller  much  trouble  and 
expense  in  having  one  kind  of  money  converted  into  another.  The 
perception  by  Newton  that  the  moon  falls  toward  the  earth  by  the 
same  law  that  an  apple  does  led  to  the  establishment  of  the  law  of 
gravitation  with  the  many  useful  consequences  that  have  resulted. 
Similarly  the  equality  of  men  before  the  law  results  in  a  general 
sense  of  security  which  is  productive  of  personal  and  social  effi- 
ciency in  many  ways. 

Aids  to  other  Efficients 

The  principles  of  diversity  and  uniformity  are  not  only  themselves 
direct  sources  of  efficiency,  but  they  also  act  in  important  ways 

130 


UNIFORMITY  AND   DIVERSITY  131 

through  the  other  Efficients.  Thus  in  order  to  teach  a  group  of 
children  at  the  same  time,  certain  uniformities  of  age,  development, 
and  interest  must  exist  among  the  individual  children  composing 
the  group.  In  other  words  special  uniformities  and  diversities 
enter  into  the  formation  of  a  group,  and  hence  into  such  particular 
forms  of  the  group,  as  reuse,  the  unit  and  multiplier,  multiplicative 
groups,  and  orders  of  material.  In  fact  we  shall  find  that  uni- 
formity and  diversity  are  the  raw  materials,  so  to  speak,  out  of 
which  groups  and  the  various  Efficients  are  formed. 

In  particular  it  is  well  to  observe  at  this  point  that  a  uniformity 
(and  its  accompanying  diversity)  in  some  cases  form  an  incipient, 
or  rude  germinal  group,  and  in  other  cases  a  specially  efficient  final 
form  of  group. 

It  will  be  noted  that  psychologically  the  perception  (and  treat- 
ment) of  diversities  precedes  that  of  uniformities;  while  logically 
the  reverse  is  often  the  case.  Hence  in  some  places  we  treat  di- 
versities before  uniformities,  and  in  other  cases  follow  the  reverse 
order. 

CLASSIFICATION  OF  DIVERSITIES 
Relations  of  Uniformity  and  Diversity 

Before  the  classification  of  diversities  and  uniformities  is  at- 
tempted, it  should  be  stated  that  a  uniformity  always  implies  a  diver- 
sity (and  vice  versa),  but  that  when  one  of  the  two  is  prominent 
as  a  source  of  efficiency  the  other  may  be  inconspicuous  or  practi- 
cally hidden.  It  is  especially  important  to  bear  this  fact  in  mind 
whenever,  for  certain  reasons,  we  shall  temporarily  treat  the  two 
categories  separately. 

It  is  useful  to  realize  that  diversities  may  exist  among  all  possible 
material  objects,  such  for  instance  as  those  catalogued  in  the  classi- 
fication sections  of  the  preceding  chapters.  It  does  not  seem  neces- 
sary to  repeat  these  lists  at  this  point. 

It  will  be  advantageous,  on  the  other  hand,  to  consider  in  some 
detail  the  classification  of  diversities  as  to  their  form. 

Spatial  Forms  of  Diversity 

As  to  space  and  its  related  categories  a  given  diversity  may  be 
partial,  entire,  or  partial  in  some  special  way,  an  example  of  the 
last  class  being  a  mottled  form.     An  illustration  of  efficiency  ob- 


132  SOURCES  OF  EFFICIENCY 

tained  by  a  positional  diversity  is  the  fact  that  the  sewing  machine 
was  made  possible  by  the  transfer  of  the  eye  from  the  blunt  to  the 
sharp  end  of  the  needle.  A  similar  instance  was  the  placing  of  a' 
rudder  in  front  of  the  aeroplane.  Spatially  also  a  diversity  may 
be  internal,  in  that  it  exists  among  the  parts  of  an  object  as  among 
the  parts  of  a  locomotive;  or  it  may  be  extermal,  in  that  it  exists 
between  one  object  and  another  external  object,  as  between  two 
locomotives. 

Numerical  and  Group  Forms 

A  given  diversity  may  be  dual  in  that  it  contains  two  elements  as 
when  objects  differ  in  both  shape  and  color;  or  triple,  as  when 
motions  differ  in  direction,  velocity,  and  duration;  or  manifold,  as 
when  two  given  objects  differ  in  size,  weight,  color,  form,  position, 
motion,  density,  utility,  and  with  respect  to  other  categories. 

Hence  it  follows  that  diversities  may  occur  in  bundles  or  groups. 
Important  cases  are  those  variations  which  in  the  process  of  evolu- 
tion occur  in  aggregates  or  groups  and  which  are  termed  saltations 
or  mutations. 

It  is  evident  also  that  diversities  may  be  grouped  multiplicatively 
in  various  ways.  Thus  the  differences  between  an  amoeba  and  a  man 
may  be  treated  as  a  multiplicative  group  system  of  differences. 

Other  Species  of  Diversity 

Again,  diversities  may  be  artificial  or  natural;  active  or  passive; 
permanent  or  temporary;  relative  or  absolute. 

A  temporary  diversity  is  a  diversity  of  diversity;  that  is,  a 
diversity  of  the  second  order. 

In  general  it  is  most  important  for  our  purpose  to  remember  that 
one  diversity  may  be  of  higher  multiplicative  order  than  another, 
and  as  a  consequence  more  vital  and  useful  in  many  ways.  Thus 
the  diversities  which  characterize  a  set  of  accounts  kept  in  the  card 
form  are  in  general  of  a  higher  order  than  those  found  among 
accounts  kept  in  the  ledger  book  form.  So  a  difference  in  the 
mental  power  of  two  men  is  many  stages  above  a  difference  in  the 
color  of  their  eyes. 

In  brief  we  may  say  a  diversity  may  be  of  high  order  because  it 
is  manifold,  or  of  several  dimensions,  or  because  it  occurs  in  ma- 
terial of  a  high  order  of  efficiency,  or  exists  between  materials  of 


UNIFORMITY  AND   DIVERSITY  133 

widely  different  orders,  or  because  the  given  diversity  produces 
especially  important  efficiency  results. 

Difficult  and  Complex  Forms 

Certain  diversities  are  so  peculiar  as  to  be  difficult  to  grasp  and 
characterize.  Illustrations  are  the  differences  between  the  proper- 
ties of  certain  alloys  and  those  of  their  constituents,  or  that  between 
matter  and  mind,  and  that  between  uniformity  and  diversity  them- 
selves. Some  of  these  diversities  may  be  so  ultimate  that  we  lack 
externality  by  which  to  determine  them;  others  of  them  are  doubt- 
less due  to  some  untraced  action  of  the  multiplicative  principle. 

The  various  species  of  diversities  may  be  complexed  together  in 
many  ways.  An  example  of  a  complex  diversity  is  that  between 
two  personalities,  or  two  civilizations,  or  two  philosophies. 

CLASSIFICATION  OF  UNIFORMITIES 

As  has  already  been  stated,  for  every  case  of  diversity  there  is  a 
corresponding  case  of  uniformity.  But  in  certain  instances  the  di- 
versity involved  may  be  prominent  while  the  related  uniformity  is 
obscure,  or  vice  versa.  Hence  cases  often  occur  where  the  one  of 
these  sources  of  efficiency  is  noteworthy,  while  the  other  is  incon- 
spicuous. Thus  certain  differences  between  the  ideas  of  space  and 
time  are  evident  but  the  connection  or  likeness  between  these  two 
concepts  is  more  difficult  to  conceive. 

It  does  not  seem  necessary  to  catalogue  and  illustrate  those  species 
of  uniformity  which  plainly  correspond  to  species  of  diversity,  such 
as  uniformities  of  color,  size,  shape,  weight,  etc.  We  shall  limit 
ourselves  therefore  to  a  consideration  of  the  cases  where  uni- 
formities are  especially  prominent  and  are  relatively  independent  of 
the  diversities  related  to  them. 

Dual  Uniformities 

Besides  the  dual  uniformity  which  consists  of  uniformity  in  two 
respects  such  as  color  and  size,  another  form  of  dual  uniformity  is 
that  which  exists  between  two  objects,  as  between  two  peas.  Among 
the  most  important  dual  uniformities  of  this  class,  are  those  equiva- 
lences between  objects  or  systems  which  are  termed  equalities, 
equations,  or  identities. 

Truth  in  one  of  its  aspects  viz. :  as  a  correspondence  between  fact 
and  symbol  is  a  dual  uniformity  of  this  general  kind. 


134 


SOURCES  OF  EFFICIENCY 


Orders  of  Uniformity 

Cases  of  uniformity  of  higher  order,  Hke  those  of  diversity, 
call  for  especial  attention.  Thus  the  uniformity  with  which  the 
earth  rotates  on  its  axis  is  more  important  than  uniformity  in  the 
speed  with  which  a  man  walks.  So  equality  of  opportunity  for 
different  men  is  of  a  higher  order  than  equality  of  physical  weight. 

Important  special  cases  of  uniformity  are  those  which  are  due  to 
some  outside  cause,  and  which  may  often  be  controlled  through  this 
cause.  An  example  is  a  likeness  in  the  mental  habits  of  pupils  due 
to  certain  qualities  in  a  teacher,  or  uniformity  in  family  traits  due 
to  heredity.  Mention  should  also  be  made  of  the  uniformity  which 
arises  when  one  set  of  forces  is  generated  in  order  to  balance  or 
counteract  another  set. 

Approximate  Uniformities 

It  is  well  to  notice  also  that  certain  so-called  uniformities  are  due 
to  limitations  in  our  powers  of  perception.  An  example  is  the 
apparent  uniformity  in  the  surface  of  a  table.  It  is  often  profitable 
to  regard  such  a  uniformity  as  a  first  group  in  a  multiplicative 
group  system. 

COMBINATIONS   OF  UNIFORMITIES   AND  DIVERSITIES 

Evidently  uniformities  and  diversities  may  be  combined  in  a  great 
variety  of  ways.  Only  the  most  important  of  these  will  be  here 
considered. 

Combinations  Related  Spatially 

(i)  In  a  given  uniformity,  the  diversities  may  be  internal.  An 
example  is  the  uniformity  of  length  during  wide  changes  of  tem- 
perature in  a  bar  formed  of  the  metal  called  invar,  due  to  the  fact 
that  the  bar  is  an  alloy  of  two  metals,  nickel  and  steel ;  or  steadiness 
of  bodily  health  due  to  the  action  of  different  organs  in  different 
ways;  or  an  equivalence  relation  of  any  sort  between  two  objects 
which  differ  in  their  composition  or  details. 

(2)  The  diversities  which  are  related  to  a  given  uniformity  may 
be  external  to  the  uniformity.  Thus  comparative  uniformity  of 
the  temperature  is  often  maintained  within  a  building  by  dividing 
the  walls  which  surround  the  building  into  several  air  chambers. 

(3)  A  special  variety  of  (2)  is  of  sufficient  importance  to  call 


UNIFORMITY  AND  DIVERSITY  135 

for  independent  mention.  The  allusion  is  to  that  form  in  which 
differences  are  distributed  more  or  less  symmetrically  about  a  mean 
or  average.  Illustrations  are  a  series  of  groups  formed  by  setting  up 
certain  standards  and  including  in  a  given  group  all  the  cases  that 
fall  within  certain  limits  above  or  below  a  given  standard.  Similar 
cases  are  the  grouping  of  places  on  the  earth's  surface  by  the  use 
of  latitude  and  longitude,  and  the  many  varieties  of  symmetry  in 
mathematics,  art,  and  common  life. 

Combinations  Otherwise  Related 

(4)  The  uniformity  and  the  diversity  which  are  combined  may  be 
of  such  a  nature  that  the  category  of  external  or  internal  does  not 
apply  to  their  relation.  As  an  example  we  have  that  combination 
of  diversity  in  space  with  uniformity  in  time  which  is  found  in 
markings  on  finger  tips  as  used  in  identifying  criminals. 

(5)  Finally  we  have  those  complex  cases  where  uniformities  and 
diversities  are  combined  in  various  ways  at  the  same  time.  Thus 
in  a  card  index  certain  diversities  are  internal  and  others  external 
to  the  uniform  size  of  the  cards.  Some  of  the  uniformities  and 
diversities  involved  are  also  temporal  in  nature.  The  result  is 
a  manifold  and  varying  system  of  groups,  productive  of  much 
efficiency. 

EFFICIENCY    FUNCTIONS    OF    DIVERSITIES 

Since  uniformities  and  diversities  are  incipient  or  special  forms  of 
groups  and  other  Efficients,  the  efficiency  functions  of  uniformities 
and  diversities  are  best  expressed  in  terms  of  those  of  the  other 
Efficients. 

Diversities  as  a  Source  of  Reuse 

In  the  first  place  it  is  to  be  observed  that  a  diversity  is  often  the 
primal  source  of  a  case  of  reuse.  For  instance  to  recur  to  a  former 
illustration  the  separation  of  the  engine  of  a  steamboat  from  the 
hull  together  with  the  transfer  of  this  engine  to  a  tugboat  leads  to 
repeated  use  of  the  engine,  and  hence  to  the  various  economies  and 
efficiencies  which  characterize  such  reuse.  To  consider  a  more 
general  case,  some  diversity  in  the  form  of  separation  of  parts  is 
evidently  essential  to  all  marginal  reuse.  Also  a  high  degree  of 
diversity  often  leads  to  a  high  degree  of  marginal  reuse.    Thus  the 


136  SOURCES  OF  EFFICIENCY 

condyle  on  which  the  head  of  a  bird  rotates  allows  much  greater 
freedom  of  motion  than  that  on  which  man's  head  is  poised;  hence 
the  work  done  by  a  bird  in  putting  its  body  in  a  given  position  is 
reused  marginally  to  a  much  greater  extent  than  is  such  work  when 
done  by  a  man. 

Diversities  also  open  the  way  to  other  forms  of  reuse.  Thus  by 
eating  a  meal  composed  of  foods  which  differ  as  to  the  time  of  their 
digestibility,  the  gastric  juice  and  whole  digestive  apparatus  may  be 
reused  in  the  process  of  assimilating  the  meal. 

Diversities  lead  to  Groups  and  Group  Systems 

Similarly  uniformities  and  diversities  lead  to  the  formation  of 
units  and  multipliers  and  of  groups  in  general.  These  groupage 
results  often  take  many  special  and  highly  important  forms.  An 
instance  is  the  discovery  by  Joseph  Henry  that  oiled  silk  will  insulate 
an  electric  wire  and  that  consequently  great  lengths  of  such  wire 
may  be  wound  around  an  iron  core  in  concentrated  form,  later 
results  being  of  course  the  invention  of  the  electric  telegraph  and 
the  dynamo.  In  like  manner  the  tubular  boiler  is  a  case  where  a 
diversity  of  material  gives  rise  to  a  concentration  of  force  in  both 
time  and  space  and  as  a  result  has  made  the  locomotive,  for 
instance,  a  practical  success. 

Not  less  important  is  the  formation  of  multiplicative  group  sys- 
tems by  the  utilization  of  diversities.  For  example  the  separation  of; 
the  continuous  manuscript  roll  into  the  equal  parts  called  leaves  led 
to  several  of  the  group  systems  which  we  find  in  a  book.  So  owing 
to  chemical  analysis  the  way  has  been  opened  to  the  systematic 
group  combination  of  elementary  substances,  the  result  being  the 
innumerable  substances  now  in  use  which  have  been  prepared  by 
chemical  synthesis. 

A  diversity  often  leads  to  the  formation  of  an  order  of  materials 
without  any  intervening  multiplicative  group  stage.  Thus  the  change 
of  seasons  in  the  Temperate  Zones  results  in  a  multiplicative  grada- 
tion of  seasons  and  of  corresponding  life  activities,  winter  being  the 
abstract  efficiency  season.  The  superiority  of  the  inhabitants  of 
the  Temperate  Zone  is  doubtless  in  large  part  due  to  this  fact  and 
its  efficiency  consequences. 


UNIFORMITY  AND   DIVERSITY  137 

l-ead  to  New  Uniformities  and  Diversities 

One  diversity  frequently  leads  to  the  formation  or  recognition  of 
another  diversity  and  its  fruits.  Thus  difference  in  soil  should 
mean  difference  in  methods  of  cultivation  and  of  products,  and 
hence  to  increased  profits  on  the  average. 

Similarly  a  diversity  may  lead  to  a  uniformity  and  its  fruits.  For 
instance  the  fluidity  which  characterizes  water  causes  the  top  of  a 
body  of  water  to  form  a  level  surface  and  manifests  itself  in  other 
useful  uniformity  properties.  Diversified  farming  makes  profitable 
returns  more  certain.  Investment  of  funds  in  several  different  ways 
adds  to  the  likelihood  of  always  having  some  income. 

An  Aid  in  Directive  Work 

Diversity  in  its  various  forms  also  facilitates  directive  efficiency 
processes.  Thus  even  the  plant  in  order  to  transfer  starch  from  one 
part  of  its  structure  to  another  converts  insoluble  starch  into  sugar 
which  can  be  dissolved  and  made  fluid.  So  in  business  fluid  capital 
of  all  kinds  is  directible.  In  another  line  of  action,  separation  or 
distinction  of  parts  opens  the  way  for  the  substitution  of  what  costs 
little  for  what  is  expensive.  Also  the  separation  of  canned  goods 
for  instance  from  surrounding  causes  of  decay  leads  to  the  efficient 
directive  action  of  these  foods  both  in  time  and  space.  The  recog- 
nition of  diversity  makes  it  easy  to  realize  the  Heedlessness  of 
throwing  out  the  baby  with  the  bath,  and  later  the  possibility  of 
developing  the  child  without  breaking  its  will. 

Absolute  Values  of  Diversity 

The  use  of  diversity  often  leads  to  certain  absolute  values ;  that  is, 
to  advantageous  results  which  transcend  the  data  incalculably,  and 
may  be  unique  in  that  they  are  not  otherwise  attainable.  Thus  if 
the  division  of  a  ship  into  compartments  leads  to  the  saving  of  the 
lives  of  the  passengers,  the  result  is  of  the  kind  just  described. 
Similarly  the  isolation  of  persons  sick  of  infectious  diseases  may 
lead  to  like  inestimable  advantages. 

Noticing  differences  in  weight  in  samples  of  supposed  nitrogen 
was  the  means  of  discovering  the  chemical  element  argon  and  later 
of  other  elements.  The  plasticity  of  maize  made  it  possible  to  de- 
velop varieties  which  ripen  in  the  short  summer  of  comparatively 
cold  climates.  A  diversity  of  parts  in  a  landscape  or  work  of  art  is 
frequently  a  source  of  both  esthetic  charm  and  commercial  value. 


138  SOURCES  OF  EFFICIENCY 

Complex  Utilities 

The  above  efficiency  functions  may  be  combined  in  various  com- 
plex ways.  An  example  is  the  great  variety  of  useful  results  which 
comes  to  the  farmer  who  makes  it  a  rule  to  keep  the  soil  thoroughly 
pulverized  about  certain  growing  crops.  These  complex  develop- 
ments may  take  extraordinary  and  unexpected  forms.  Thus  from 
the  chance  observation  that  light  makes  a  smudge  on  silver  has 
sprung  the  whole  science  and  art  of  photography.  From  the  fact 
that  rubbed  amber  attracts  a  feather  has  arisen  all  of  electrical 
science.  Of  similar  complex  and  dialectic  character  are  the  advan- 
tages which  have  resulted  respectively  from  the  ownership  of  prop- 
erty in  severalty,  from  the  division  of  labor,  and  from  the  atomic; 
theory  of  matter. 

Words  Illustrating  Usefulness  of  Diversities 

The  benefits  obtainable  by  the  use  of  diversities  may  be  realized 
in  another  often  effective  way,  viz.:  by  realizing  the  useful  results 
connected  with  certain  more  or  less  special  and  familiar  forms  of 
diversity  such,  for  instance,  as  analysis,  variety,  solution,  indepen- 
dence, detachment,  ductility,  delicacy,  sensitiveness,  freedom.  The 
advantages  connected  with  diversity  may  also  be  realized  in  a  nega- 
tive way  by  recalling  the  evils  and  losses  suggested  by  such  words 
as  fixity,  monotony,  and  fossilism.  A  concrete  example  is  a  railroad 
accident  caused  by  color  blindness  in  an  engineer. 

Limitations  to  Values  of  Diversity 

The  presentation  of  the  efficiency  functions  of  diversities  should 
not  be  closed  without  a  statement  concerning  the  dangers  and  evils 
connected  with  the  use  of  diversities.  Too  much  diversity,  or  mis- 
placed diversity,  may  result  in  the  impairment  or  destruction  of 
groups,  or  in  difficulty  in  their  formation.  An  example  is  the 
diversity  which  characterizes  a  routed  army.  Another  illustration 
is  furnished  by  the  evil  results  of  too  pronounced  a  division  of 
labor.  Often  extreme  diversities  result  in  what  is  called  license 
or  chaos. 

EFFICIENCY  FUNCTIONS  OF  UNIFORMITIES 
Uniformity  as  a  Source  of  Reuse 

Uniformities  also  have  their  characteristic  efficiency  functions. 
Thus  the  fact  that  the  ocean  is  approximately  the  same  the  world 


UNIFORMITY  AND   DIVERSITY  139 

over  leads  to  reuse  in  all  other  places  of  knowledge  of  it  gained  in 
any  given  place.  The  same  statement  applies  to  the  atmosphere,  a 
geological  stratum,  or  human  nature.  Permanence  in  time,  gained 
for  instance  by  printed  or  phonographic  records,  or  by  monuments, 
leads  to  the  reuse  of  work  and  facts.  The  discovery  by  Van  t'Hoff 
that  liquids  and  gases  have  important  properties  in  common  has  led 
to  the  reuse  of  our  knowledge  of  one  with  respect  to  the  other  in 
important  cases. 

Basis  of  Groups  and  Group  Systems 

Similarly  a  uniformity  may  be  the  basis  of  a  group  formation  of 
some  sort,  and  hence  be  the  source  of  the  advantages  which  come 
from  the  use  of  the  group.  For  example,  if  a  field  is  approximately 
level,  this  uniformity  opens  the  way  to  the  use  of  a  gangplow  in 
cultivating  the  field.  Uniformity  in  the  size  and  quality  of  a  manu- 
factured article  leads  to  the  wide  use  of  that  article.  Justice  and 
honesty  are  the  sources  of  many  similar  beneficial  results. 

The  invariability  in  the  time  occupied  by  the  earth  in  rotating  once 
on  its  axis  is  the  basis  of  our  multiplicative  group  system  of  time 
measurement  with  its  many  ramifying  utilities.  Similarly  various 
social,  political,  and  indeed  all  group  systems  are  founded  on  certain 
uniformities. 

Other  Uses  of  Uniformities 

Uniformity  and  continuity,  when  realized,  often  make  the  use  of 
certain  kinds  of  externality  comparatively  easy.  An  example  is  the 
manufacture  of  an  article  on  a  large  scale  when  the  demand  for  the 
object  is  certain  and  permanent. 

Uniformities  frequently  open  the  way  to  profitable  directive  acts. 
Thus  uniformities  in  the  parts  of  a  watch  or  automobile  facilitate 
the  substitution  of  a  new  part  for  any  part  that  may  be  broken  or 
worn  out.  If  we  know  that  a  certain  volume  of  gas  will  give  as 
much  energy  as  a  ton  of  coal  the  substitution  of  one  for  the  other 
is  often  the  source  of  valuable  efficiencies.  The  fact  that  a  network 
of  protoplasm  connects  the  cells  in  a  plant  makes  possible  the  opera- 
tion of  botanical  grafting. 

The  use  of  uniformities  as  of  diversities,  in  certain  cases  has 
transcendental  or  absolute  value,  such  as  those  of  saving  life,  or 
giving  knowledge  otherwise  unattainable. 


I40  SOURCES  OF  EFFICIENCY 

Complex  and  Self-developing  Values 

The  advantages  resulting  from  the  use  of  uniformity  also  often 
take  a  complex  and  self -developing  form.  Such  for  instance  are  the 
uses  made  of  the  straightness  of  a  ray  of  Hght,  or  the  advantages 
arising  from  uniformity  in  weights  and  measures,  or  in  language,  or 
from  the  correspondence  of  an  organism  to  its  environment.  Some- 
times these  benefits  are  in  part  negative.  Instances  are  the  results 
obtained  from  applications  of  the  law  of  conservation  of  energy,  or 
from  the  principle  that  action  and  reaction  are  always  equal. 

Words  Illustrating  the  Usefulness  of  Uniformities 

We  are  aided  in  realizing  the  aggregate  of  efficiency  values  in 
uniformities  by  noting  those  connected  with  certain  special  cate- 
gories of  uniformity  as  for  instance  with  honesty,  justice,  constancy, 
reliability,  perseverance,  durability,  etc.;  or  by  trying  to  grasp  the 
inefficiency  that  would  characterize  the  world  life  if  carried  on 
without  the  aid  of  these  and  similar  categories. 

Limitations  to  the  Utilities  in  Uniformities 

The  use  of  uniformities  however  often  brings  certain  drawbacks 
or  compensations.  This  fact  may  be  realized  by  noting  for  instance 
the  evils  connected  with  such  words  as  monotony,  fashion,  custom, 
panic,  socialism.  Ambiguities  are  an  illustration  of  another  class  of 
evils  connected  with  the  uniformity  category.  An  important  case  of 
the  misuse  of  the  principle  of  uniformity  is  what  is  termed  hasty 
generalization.  This,  in  brief,  consists  of  jumping  to  the  con- 
clusion that  what  is  true  in  one  or  a  few  cases  is  true  in  all  cases 
of  a  given  class. 

The  most  important  error  of  this  kind  is  that  of  regarding  some 
special  form  of  uniformity,  such  as  reality  or  substance,  or  more 
specifically  matter,  force,  mind,  or  some  other  species  of  reality 
uniformity  taken  as  fundamental  and  inclusive,  as  the  only  route  to 
efficiency  results.  This  view  often  leads  to  the  further  error  of  re- 
garding uniformity  in  some  form  (as  in  that  often  termed  truth)  as 
more  fundamental  and  important  than  the  uses  of  uniformity. 
Errors  of  this  class  will  be  treateed  in  more  detail  later. 

Human  Progress  an  Advance  in  Uniformities  and  Diversities 

After  what  has  been  said  as  to  the  various  efficiency  values  of 
uniformity  and  diversity,  it  is  not  surprising  to  note  that  progress 


UNIFORMITY  AND  DIVERSITY  141 

in  each  department  of  knowledge  and  action  has  been  marked  by  a 
progressive  development  of  uniformities  and  diversities,  both  in 
number  and  in  degree  of  efficiency  power.  The  child's  mind  begins 
its  unfolding  process  by  the  perception  of  differences  and  similari- 
ties, and  progresses  by  penetrating  to  and  grasping  diversities  and 
uniformities  which  are  ever  more  comprehensive  and  vital.  The 
beginning  of  abstract  and  formal  science  is  probably  to  be  found  in 
the  first  perception  by  man  of  the  difference  between  fixed  stars  and 
planets,  and  all  subsequent  astronomical  progress  may  be  regarded 
as  a  mere  development  of  continuously  better  uniformities  and  di- 
versities, leading  to  the  generation  of  ever  more  efficient  systems  of 
mutiplicative  groups.  A  similar  process  has  characterized  progress 
in  every  department  of  human  life  and  thought,  and  hence  progress 
as  a  whole. 

EFFICIENCY  ANALYSIS   OF  UNIFORMITIES  AND  DIVERSITIES 

In  order  to  make  the  most  efficient  use  of  uniformities  and 
diversities  it  is  important  to  analyze  these  concepts  as  closely  as 
possible,  especially  in  terms  of  the  other  Efficients. 

Relations  to  the  Group  Principle 

With  respect  to  the  group  principle,  in  general  every  diversity 
means  a  new  unit  and  hence  often  an  order  of  units;  every  uni- 
formity means  a  new  tie,  or  combination  of  units.  Hence,  from  one 
point  of  view,  the  diversity  and  uniformity  aspects  are  the  two 
halves  of  the  group  concept. 

Also  it  has  already  been  remarked  that  uniformities  and  diversities 
sometimes  serve  as  crude,  incipient  groups,  and  at  other  times  as 
final  highly  finished  groups.  Hence  from  these  various  points  of 
view  uniformity  and  diversity  are  to  be  regarded  primarily  as  a 
stage  in  the  multiplicative  system  of  things. 

This  method  of  regarding  uniformities  and  diversities  explains 
why  an  animal,  as  a  zebra,  may  be  marked  in  a  very  peculiar  way, 
and  yet  be  protected  by  its  environment.  For  owing  to  our  habit  of 
seeing  things  in  groups,  if  the  animal's  markings  fit,  not  its  environ- 
ment in  all  respects,  but  merely  some  one  of  the  many  group  sys- 
tems of  which  the  environment  is  composed,  we  shall  be  likely  to  see 
the  animal  as  a  part  of  this  one  system  and  not  as  distinct  from  its 
surroundings.     The  multipHcative  view  of  uniformity  and  diversity 


142  SOURCES  OF  EFFICIENCY 

as  contrasted  with  the  vague,  lumpish  view  often  taken  has  many- 
other  advantages. 

In  uniformities  and  diversities  the  group  principle  involved  is 
built  around  with  certain  auxiliary  categories,  or  efficiency  handles, 
which  should  at  least  be  mentioned. 

Relations  to  other  Concepts  and  Efficients 

As  to  the  number  idea,  we  find  an  implication  at  least  of  duality  in 
every  uniformity;  for  a  uniformity  implies  a  comparison  with 
some  other  entity  taken  as  a  standard.  Similarly  a  difference  im- 
plies at  least  two  compared  objects.  This  duality  in  a  uniformity  or 
diversity  has  certain  uses  since,  in  effect,  one  of  the  two  objects 
constitutes  an  externality  to  the  other. 

Externalities  of  another  nature  are  often  implied  in  a  uniformity 
or  diversity.  Thus  the  evenness  of  the  surface  of  a  body  of  water  is 
the  resultant  or  intersection  of  two  opposite  sets  of  forces,  those 
which  draw  objects  together,  and  those  which  often  cause  objects  to 
repel  each  other.  So  the  peculiar  individuality  of  any  object,  as  of 
a  piece  of  gold,  is  due  to  the  convergence  in  the  object  of  several 
qualities  or  properties  which  are  present  in  many  other  objects  be- 
sides gold,  and  hence  in  a  measure  are  external  to  the  gold.  Simi- 
larly any  quality  of  an  object  may  often  be  regarded  as  the  focus  of 
several  widely  existent  elements. 

Uniformities  and  diversities  imply  or  depend  on  certain  limita- 
tions. Thus  objectively  every  uniformity  is  hedged  in  by  certain 
diversities,  and  correspondingly  every  diversity  by  uniformities. 
Subjectively,  the  efficiency  of  uniformities  and  diversities  is  limited 
by  the  degree  in  which  we  are  cognizant  of  them.  Hence  in  this  and 
other  ways  much  relativity  arises  in  their  application. 

Certain  other  relations  between  uniformities  and  diversities 
should  be  mentioned.  Thus  with  respect  to  order,  as  already  stated, 
diversity  as  a  rule  comes  first  psychologically,  while  uniformity  is 
first  logically.  With  respect  to  the  principle  of  orders  of  material, 
diversity  is  more  concrete  (therefore  individual  and  qualitative), 
uniformity  more  abstract.  With  respect  to  force,  diversity  is  more 
active,  and  uniformity  more  passive. 

Diversity  relates  primarily  to  quality,  uniformity  to  quantity. 

In  relation  to  the  idea  of  efficiency,  diversity  is  directly  essential 
to  this  idea  (since  efficiency  means  surplusage)  while  uniformity  is 
an  indirect  route  to  it. 


UNIFORMITY  AND  DIVERSITY  143 

Definitions 

The  terms  in  current  use  for  various  kinds  of  uniformity  and 
diversity  are  loose,  overlap,  and  are  often  difficult  of  precise  defini- 
tion and  coordination.  However  in  the  course  of  different  discus- 
sions it  is  frequently  necessary  to  use  some  of  these  terms,  and  it  is 
therefore  important  to  define  them  as  accurately  as  possible  with 
reference  to  uniformity  and  diversity  as  sources  of  efficiency. 

The  following  are  among  the  most  important  terms  of  the  uni- 
formity class. 

Uniformity  means  primarily  oneness  of  form,  amid  various  diver- 
sities such  as  those  of  position,  material,  color.  Hence  it  is  pri- 
marily a  spatial  uniformity.  However  its  meaning  is  often  refined 
and  extended  so  as  to  include  almost  every  kind  of  oneness.  Thus 
we  may  speak  of  objects  as  uniform  in  color  or  in  any  other  quality. 
Equivalence  means  primarily  sameness  with  respect  to  weight; 
stated  more  generally  it  means,  equally  availing.  Hence  it  is  pri- 
marily a  dynamic  term.  As  often  used  however  it  has  outgrown  its 
original  limited  significance. 

Continuity  means  literally  a  holding  together  (against  opposing 
forces).  Hence  it  has  spatial  and  negative  dynamic  aspects.  It  is  a 
relation  without  gaps,  that  is,  an  unbroken  relation,  and  usually 
contrary  to  certain  appearances.  It  may  also  be  one,  two,  or  three 
dimensional. 

Similar  efficiency  descriptions  might  be  given  of  other  terms 
belonging  to  this  general  class  such  as  accuracy,  analogy,  adapta- 
tion, conservation,  consistency,  constancy,  consecutivity,  certainty, 
equality,  evenness,  homogeneity,  immobility,  identity,  likeness,  mo- 
notony, monism,  necessity,  oneness,  persistence,  parallelism,  parity, 
reality,  reliability,  resemblance,  similarity,  stability,  simultaneity, 
sameness,  truth,  unity. 

Of  terms  in  the  diversity  class  the  following  call  for  particular 
mention. 

Diversity  means  literally  a  bearing  or  turning  apart.  Hence  the 
term  originally  had  a  dynamic  as  well  as  a  spatial  aspect.  But  in 
its  present  generalized  form  it  may  be  used  to  express  almost  any 
difference. 

Change  means  diverse  forms  of  the  same  object  occurring  in 
succession.  Hence  it  involves  an  element  of  time.  Its  meaning  in 
other  respects  is  vague  and  general. 


144  SOURCES  OF  EFFICIENCY 

Similar  efficiency  descriptions  might  be  given  of  the  other  di- 
versity terms  in  current  use  such  as  of  alteration,  conversion,  devia- 
tion, discontinuity,  dissimilarity,  flexibility,  fluidity,  freedom, 
heterogeneity,  instability,  manyness,  mobility,  modification,  muta- 
tion, plasticity,  relativity,  sensitiveness,  unevenness,  unlikeness, 
variation,  variety. 

METHODS  OF  APPLICATION 
Group  View  an  Aid 

The  view  of  uniformity  as  not  mere  vague  lumpish  likeness  and 
of  diversity  as  not  accidental  or  capricious  difference,  but  of  both 
as  essentially  groupish  in  nature,  and  when  taken  together,  as  form- 
ing certain  useful  stages  in  the  multiplicative  system  of  things,  is  an 
important  aid  in  using  these  instruments  in  the  most  efficient  way. 

Great  Number  of  Forms 

Thus  the  multiplicative  view  is  an  aid  in  realizing  the  vast  num^ 
ber  of  diversities  and  uniformities  which  exist  or  may  be  generated. 
For  example  in  order  to  form  some  idea  of  the  different  kinds  of 
apples  which  are  possible  we  may  consider  the  following  product : 

(no.  possible  sizes)   X   (no.  shapes)   X   (no.  colors)   X 
(no.  flavors)  X  (no.  durations). 

It  is  also  well  to  remember  that  some  of  the  above  factors  are  also 
multiplicative  group  systems.  Such  a  method  of  treating  diversi- 
ties enables  the  farmer  for  instance  to  forecast  the  great  variety 
of  ways  in  which  a  horse  or  fertilizer  rnay  be  defective,  or  a  teacher 
to  grasp  the  immense  diversity  in  young  minds,  and  of  methods 
and  devices  which  may  be  employed  to  meet  special  needs. 

Illustrations  of  Extreme  Cases 

In  reinforcement  of  the  above  conception  it  is  important  to  bear 
in  mind  certain  facts  or  principles  like  the  following:  The  divisi- 
bility of  matter  is  practically  without  limit,  for  the  molecules  in  a 
cubic  centimeter  of  gas  if  placed  in  line  would  go  many  times  round 
the  world  and  would  take  265  billions  of  years  to  count  and  yet  a 
molecule  is  composed  of  many  ions.  Also  different  kinds  of  matter 
interfuse  so  that  it  is  said  that  "a  perfectly  pure  chemical  element  is 
the  dream  of  the  ignoramus".    Also  relations  of  kinds  of  matter  are 


UNIFORMITY  AND  DIVERSITY  145 

in  a  constant  state  of  change  since  motion  is  the  normal  law  of  the 
universe.  Even  the  force  of  gravitation  on  the  surface  of  the 
earth  is  constantly  changing  as  the  earth  shifts  its  position  with 
reference  to  the  sun  and  moon.  The  number  of  diversities  man  can 
create  or  conceive  of  in  like  manner  is  without  limit  since  for  in- 
stance the  grey  matter  of  the  human  brain  contains  5,ooo,ocx),ooo 
cells  each  of  which  apparently  may  be  a  center  or  modifier  of  idea- 
tion in  many  ways.  A  cubic  millimeter  of  blood  contains  5,000,000 
red  corpuscles,  or  the  blood  in  a  human  body  on  the  average  con- 
tains 22,500,000,000,000  of  them,  and  with  changes  in  these,  the 
bodily  health  and  mental  processes  vary. 

With  respect  to  uniformity  no  one  as  yet  has  been  able  to  discover 
a  variation  in  the  atomic  weight  of  any  chemical  element.  In  color 
photography  of  a  certain  kind,  two  successive  laminae  in  a  gelatine 
plate  are  separated  by  a  distance  of  only  one  one  hundredth  mil- 
lionth of  an  inch,  yet  those  laminae  retain  their  exact  position  dur- 
ing the  process  of  applying  chemical  solutions  to  fix  them.  We  also 
have  the  general  principle  of  continuity,  often  embodied  in  the 
statement  that  nature  never  proceeds  per  saltum. 

The  principle  of  multiplying  relations  also  enables  us  to  realize 
the  extraordinary  power  in  a  small  diversity.  Thus  a  difference  of 
one-tenth  of  one  per  cent  in  the  amount  of  carbon  in  steel  may 
render  worthless  an  otherwise  good  piece  of  metal. 

The  Multiplicative  Principle  an  Aid  in  Other  Ways 

The  multiplicative  principle  also  aids  us  in  utilizing  crude  and 
imperfect  uniformities  and  diversities  when  better  forms  are  not 
available.  For,  as  has  been  pointed  out  in  other  connections,  the 
multiplicative  principle  in  a  measure  is  both  self  corrective  and  has 
the  power  to  develop  the  imperfect  into  something  better.  An 
illustration  is  the  use  in  combination  of  our  crude  theory  of  atoms 
(or  diversity)  and  the  ether  (or  unity)  and  the  vast  number  of, 
useful  results  thus  obtained.  A  still  broader  case  is  the  employment 
together  of  monistic  and  pluralistic  theories  as  toolage  aspects  of 
the  universe. 

Externality  an  Aid  to  Greater  Results 

Externality  is  often  a  powerful  aid  in  discovering  a  uniformity 
or  diversity  in  a  difficult  situation.    For  within  a  large  area  of  facts, 


146  SOURCES  OF  EFFICIENCY 

one  is  more  likely  to  find  a  spot  or  spots  where  some  important 
diversity  or  uniformity  is  unmasked  and  exposed  to  view  than  in  a 
narrow  area.  So  subjectively  the  externalities  afforded  by  a  broad 
education  or  by  wide  travel  are  fitted  to  break  up  the  permanences 
of  habit  and  tradition. 

To  look  at  the  matter  in  more  detail,  the  externality  of  time  has 
enabled  men  to  discover  the  change  in  position  of  many  so-called 
fixed  stars,  and  to  learn  that  mountains  rise  and  fall,  and  that  some 
rivers  are  more  stable  than  mountains.  So  the  externality  of  travel 
and  study  enabled  Darwin  and  Wallace  to  establish  the  fact  of  the 
variation  of  species  and  to  assign  an  adequate  reason  for  the  same. 
By  the  aid  of  the  gelatine  culture  plate  Koch  was  able  to  isolate 
different  species  of  bacteria.  Externality  in  the  form  of  a  fly  wheel 
may  give  uniformity  and  continuity  to  the  motion  of  an  otherwise 
unstable  machine. 

A  more  abstract  form  of  externality  in  this  connection  is  that 
whereby  we  get  a  diversity  by  the  use  of  another  intermediate  di- 
versity as  when  we  form  a  conception  of  a  new  kind  of  space  by 
analyzing  the  ordinary  space  concept  into  its  essential  elements  and 
varying  or  changing  one  or  more  of  these  elements. 

Treatment  of  Difficult  Cases 

In  forming  or  discovering  diversities  in  difficult  cases  it  is  often  a 
help  to  try  to  obtain  a  diversity  with  respect  to  certain  important 
categories  taken  in  succession.  Thus  in  such  cases  attempts  may  be 
made  successively  to  form,  for  instance,  diversity  as  to  space,  quan- 
tity, number,  or  time;  or  a  diversity  of  velocity,  force,  order,  color, 
mentality,  or  any  other  quality  or  category.  A  similar  remark 
applies  to  uniformities. 

It  may  also  be  well  to  remark  at  this  point  that  the  discovery  of 
diversities  usually  precedes  that  of  uniformities. 

In  this  connection  something  should  also  be  said  as  to  the  impor- 
tance of  determining  whether  to  give  a  uniformity  or  a  diversity  the 
leadership  in  a  given  situation,  which  species  of  each  to  use,  and 
how  best  to  combine  them.  For  instance  it  is  sometimes  necessary 
to  decide  whether  it  is  best  to  put  all  of  one's  eggs  in  one  basket  (as 
in  making  investments)  ;  or  to  determine  whether,  in  a  given  case,  to 
live  each  day  by  itself,  or  to  treat  life  as  a  whole.  Externality, 
especially  the  externality  of  consequences,  is  useful  in  such  cases. 


UNIFORMITY  AND  DIVERSITY  147 

Other  Efficients  as  Aids 

The  various  categories  of  efficiency  which  have  been  investigated 
in  the  preceding  chapters,  as  well  as  those  which  are  to  be  studied 
in  the  chapters  which  follow,  may  also  be  used  to  advantage  in  con- 
nection with  uniformities  and  diversities.  Thus  it  is  well  to  remem- 
ber that  it  is  advantageous  to  master  and  reuse  certain  important 
types  of  uniformity  and  diversity,  and  also  that  every  case 
of  reuse  produces  a  uniformity  along  its  path.  Again  by  the  appli- 
cation of  predictive  reuse  we  realize  that  certain  uniformities  and 
diversities  are  in  a  sense  omnipresent.  Thus  we  may  argue  that, 
in  order  to  survive,  every  organism  must  reach  a  certain  level  of 
efficiency.  Hence  we  may  anticipate  that  every  existing  organism 
possesses  its  own  characteristic  instruments  for  obtaining  results; 
that  this  instrumentalism  differs  widely  in  its  forms  but  approxi- 
mates a  certain  uniformity  of  power. 

The  method  of  multiplicative  groups  is  also  an  aid  in  grasping 
(or  inventing)  a  large  variety  of  uniformities  or  diversities  and  in 
selecting  that  particular  one  in  the  array  which  is  best  fitted  for  a 
given  purpose.  It  also  leads  to  the  use  of  uniformities  and  diversi- 
ties in  other  and  more  aggressive  ways.  Negatively  it  prevents  the 
ignoring  and  dread  of  using  the  profusion  of  uniformities  and  di- 
versities which  exist. 

It  is  also  important  to  apply  the  principle  of  orders  of  material 
to  uniformities  and  diversities  as  an  aid  in  discriminating  between 
higher  and  lower  forms.  Thus  the  caste  system  of  India  is  charac- 
terized by  a  uniformity  and  diversity  both  of  which  are  of  a  low 
order.  For  the  uniformity  involved  is  so  concrete  and  fixed  that  it 
interferes  with  useful  change,  while  the  diversity  is  of  such  a  nature 
that  it  prevents  uniformity  of  reward  for  efficient  action.  Another 
illustration  of  somewhat  different  kind  is  the  contrast  between  the 
kind  of  diversities  which  are  utilized  when  a  drug  is  dissolved  and 
absorbed  through  the  stomach  and  general  fluids  of  the  body,  and 
the  diversities  which  are  involved  when  the  drug  is  first  ionized 
outside  of  the  body  and  then  driven  by  an  electric  current  into  that 
particular  part  of  the  organism  where  it  is  needed.  The  former 
method  because  of  the  many  unnecessary  disturbances  which  it 
produces  (that  is,  its  lack  of  uniformity)  must  be  regarded  as  of  a 
distinctly  lower  order  of  efficiency  than  the  latter. 

In  connection  with  the  limitations  which  hem  in  the  useful  func- 
tions of  uniformity  and  diversity  (see  pp.  138,  140)  it  is  well  to 


148  SOURCES  OF  EFFICIENCY 

remember  that  in  many  domains  a  certain  average  or  normal  degree 
of  uniformity  and  diversity  are  desirable.  Thus  in  certain  rela- 
tions the  peculiarities  or  bizarre  features  of  the  English  system  of 
weights  and  measures  make  it  more  highly  educative  than  the  more 
uniform  metric  system.  A  similar  remark  applies  to  the  English 
language  as  compared  with  an  artificial  language  such  as  Ido  or 
Esperanto. 

Ideal  Species 

Finally,  it  is  well  to  realize  and  work  toward  the  ideal  system  of 
uniformities  and  diversities.  For  our  purpose  this  consists  of  uni- 
formities and  diversities  in  one  or  more  of  the  Efficients,  applied  in 
efficiental  ways,  for  efficiental  ends. 

It  is  also  well  to  have  constantly  in  mind  the  best  form  of  uni- 
formities and  diversities  which  is  directly  applicable  to  affairs  in 
general.  This  consists  of  uniformities  and  diversities  combined  as 
a  multiplicative  group  system  and  in  such  a  way  that  each  uniformity 
will  interfere  with  the  diversities  to  the  least  possible  extent,  and 
vice  versa.  Contrasted  with  absolutism  at  one  extreme  and  laissez- 
faire  individualism  at  the  other,  the  form  just  described  constitutes 
a  federal  system  characterized  by  the  utmost  freedom  and  the  utmost 
law  and  order.  Practical  success  of  a  high  order  in  any  calling  con- 
sists primarily  in  realizing  the  enormous  number  of  diversities  in- 
volved, the  great  number  of  uniformities  or  ways  in  which  groups 
may  be  formed,  and  in  uniting  and  utilizing  these  diversities  and 
uniformities  by  means  of  multiplicative  group  systems  of  a  higher 
order. 

Summation  of  the  Chapter 

A  condensed  statement  of  the  principles  discussed  in  this  chapter 
will  now  be  of  service.  The  perception  and  use  of  uniformities  and 
diversities  form  a  source  of  efficiency  which  is  often  of  fundamental 
importance.  Owing  to  their  general  and  comprehensive  nature,  the 
principles  under  discussion  exist  in  a  multitude  of  forms,  though 
much  study  is  often  necessary  to  uncover  certain  of  these.  The 
simple  and  complex  forms  which  they  assume  are  alike  numerous. 

Uniformities  and  diversities  in  some  cases,  in  essence  constitute 
crude,  incipient  groups;  in  other  cases  they  are  a  highly  finished 
final  form  of  the  group.     Consequently  in  all  cases  they  have  the 


UNIFORMITY  AND  DIVERSITY  149 

efficiency  properties  of  groups  in  special  forms.  They  are  especially 
useful  as  first  steps  in  developing  more  elaborate  efficiency  organi- 
zations or  processes.  Often,  apart  from  any  consideration  of  the 
group  idea,  uniformities  and  diversities  lead  directly  to  reuse  and 
other  forms  of  efficiency  and  even  to  transcendent  results.  Numer- 
ous more  or  less  familiar  words  like  analysis  and  mobility  illustrate 
the  uses  of  diversity;  and  similarly  words  like  justice  and  reliability 
suggest  the  values  in  uniformity.  The  progress  of  the  individual 
and  that  of  the  human  race  alike,  are  marked  by  the  perception  and 
use  of  more  and  more  vital  and  comprehensive  uniformities  and 
diversities. 

The  general  multiplicative  principle  is  an  aid  in  realizing  both  the 
vast  number  of  kinds  of  uniformities  and  diversities  and  the  ex- 
treme forms  which  these  may  take.  The  self -developing  and  self- 
corrective  powers  inherent  in  the  multiplicative  principle  also  con- 
stitute an  aid  in  using  crude  forms  of  uniformities  and  diversities. 
It  is  important  to  be  able  to  realize  the  highest  types  of  resem- 
blances and  differences,  and  to  use  these  with  the  utmost  effective- 
ness. Especially  important  is  it  to  realize  that  the  highest  species 
of  all  is  the  combination  of  those  uniformities  and  diversities  which 
are  individually  most  efficient,  which  aid  each  other  the  most,  and 
interfere  with  each  other  the  least. 


EXERCISE  8 

1.  Give  an  example  of  each  of  the  principal  species  of  diversity. 

2.  Also  of  each  of  the  principal  species  of  uniformity. 

3.  State  some  of  the  advantages  in  having  two  engines  in  a  factory 
instead  of  a  single  larger  engine. 

4.  Give  a  similar  instance  where  duality  is  the  source  of  efficiency. 

5.  State  some  of  the  advantages  in  being  able  to  separate  water  into 
small  particles  of  vapor. 

6.  State  the  uniformities  and  diversities  which  enter  into  the  structure  of 
a  Zeppelin  airship. 

7.  State  some  of  the  advantages  which  follow  from  the  fact  that  the  action 
of  one  force,  as  gravitation,  is  independent  of  that  of  another,  as  light 
or  heat. 

8.  In  some  factories  the  accounts  for  the  year  are  kept  in  terms  of 
thirteen  periods  of  four  weeks  each  (instead  of  the  twelve  calendar 
months).    State  the  advantages  in  this. 

9.  Ascertain  some  of  the  peculiarities  of  different  kinds  of  Jena  glass, 
and  the  corresponding  efficiency  properties. 


150  SOURCES  OF  EFFICIENCY 

10.  Define  each  of  the  following  terms  with  reference  to  the  principle  of 
diversity,  and  give  an  example  of  the  efficiency  value  of  each:  flexibility, 
plasticity,  mobility,  adjustability. 

11.  In  a  very  dry  summer  at  the  Kansas  Experiment  Station,  on  ground 
prepared  merely  by  disking,  only  4  bushels  of  wheat  per  acre  were  produced. 
On  ground  deeply  plowed  and  thoroughly  pulverized,  the  yield  was  38 
bushels  per  acre.  If  the  cost  of  cultivation  per  acre  in  the  two  cases  was 
$.75  and  $4  respectively,  and  the  wheat  produced  was  worth  90c  per  bushel, 
what  would  have  been  the  gain  from  the  more  thorough  pulverization  of 
1000  acres? 

12.  Give  in  detail  some  of  the  advantages  in  thorough  pulverization  of 
the  soil  in  raising  crops. 

13.  Describe  the  block  system  of  managing  a  railroad,  and  state  some  of 
its  advantages.  What  elements  of  uniformity  and  diversity  are  here 
involved  ? 

14.  What  are  the  advantages  to  a  large  railroad  company  in  having  all 
the  stationery  used  in  its  offices  reduced  to  a  few  standard  types? 

15.  State  some  of  the  advantages  in  knowing  that  the  different  forms  of 
energy  in  action  on  the  earth's  surface  are,  with  slight  exceptions,  trans- 
formed sun  force. 

16.  Give  some  of  the  advantages  of  regarding  a  given  form  of  work, 
as  that  of  laying  brick,  as  a  succession  of  parts  or  motions. 

17.  In  what  ways  does  the  use  of  machines  give  uniformity  and  accuracy? 
Show  that  this  uniformity  is  sometimes  excessive. 

Give  an  example  where  a  diversity  leads  to 

18.  Marginal  reuse  22.  Another   diversity 

19.  Prophetic  reuse  23.  A  uniformity 

20.  Formation  of  a  group  24.  A  useful  directive  act 

21.  Of  a  multiplicative  group  system      25.  A  transcendent   result 

2.(i.  Complex  self -developing  results 
2'].  Give   examples   where   uniformities   produce   the    results    indicated   in 
Exs.  18-26. 

28.  Give  an  example  where  a  diversity  is  obtained  by  the  use  of  externality. 

29.  Where  a  uniformity  is  obtained  by  externality. 

30.  State  the  advantages  in  preparing  lumber  in  pieces  of  small  thickness 
and  nailing  these  together  when  heavier  pieces  are  needed.  Also  state  the 
disadvantages. 

31.  State  some  of  the  different  ways  in  which  the  lights  of  light  houses 
differ,  and  also  state  the  resulting  advantages.  Why  are  light  ships  or 
buoys   sometimes  used  instead   of  light  houses? 

32.  By  what  means  is  the  effect  of  solid  space  produced  by  a  flat  picture? 

33.  In  terms  of  the  Efficients  studied  thus  far,  state  the  efficiency  advan- 
tages of  honesty. 

34.  Give  an  example  where  an  excessive  amount  of  diversity  results  in 
loss. 

35.  Another  where  diversity  misused  in  some  other  way  results  in  loss. 

36.  Where  an  excessive  amount  of  uniformity  results  in  loss. 


UNIFORMITY  AND   DIVERSITY  151 

yj'  Where  uniformity  misused  in  some  other  way  results  in  loss. 

38.  State  some  of  the  disadvantages  which  result  from  the  fact  that  the 
gold  dollar  fluctuates  in  value.  Suggest  some  means  by  which  this  evil 
might  be  diminished,  if  not  altogether  remedied. 

39.  How  are  the  values  of  the  uniformity  and  diversity  principles  illus- 
trated by  the  use  of  the  wheel? 

40.  What  uniformity  and  diversity  principles  are  illustrated  in  a  cream 
separator? 

41.  Why  is  it  that  a  snake  can  swallow  an  object  larger  than  its  own 
head  (thus  a  boa  constrictor  can  swallow  a  calf)  ? 

42.  If  each  State  in  the  United  States  should  have  a  different  system  of 
weights  and  measures  point  out  some  of  the  disadvantages  which  would 
result. 

43.  How  does  the  principle  of  diversity  help  give  sea  power  the  superiority- 
over  land  power? 

44.  Explain  standard  time  with  reference  to  uniformity  and  diversity- 
principles. 

45.  Arthur  Young  says  "the  magic  of  property  turns  sand  into  gold". 
State  the  source  of  efficiency  which  is  involved  in  this  case. 

46.  Give  an  example  where  two  diversities  are  combined  to  form  a 
uniformity. 

47.  Also  where  two  diversities  when  combined  make  a  greater  diversity. 

48.  Discuss  the  value  of  accuracy  in  terms  of  the  other  Efficients. 

49.  State  some  of  the  advantages  of  isolating  oneself  or  one's  employees 
from  distractions  when  at  work.  Give  also  instances  where  such  isolation 
results  in  loss. 

50.  Give  an  example  showing  the  value  of  knowing  that  action  and  re- 
action are  always  equal. 

51.  What  is  meant  by  uniformity  of  the  laws  of  nature?  Illustrate.  Also 
give  three  illustrations  of  the  efficiencies  which  result  from  the  utilization 
of  this  uniformity. 

52.  Illustrate  the  advantages  which  result  from  the  fact  that  the  atomic 
weights  of  the  chemical  elements  do  not  vary. 

53.  State  the  successive  kinds  of  freedom  which  have  been  obtained  by 
the  people  of  the  United  States,  and  the  new  groupings  and  other  advantages 
which  have  resulted  from  each. 


CHAPTER  IX 

EXPENDITURES  AND  RESULTS 

General  Statement 

In  Chapters  II  to  VIII  primary  attention  has  been  paid  to 
methods  by  which  to  attain  increased  efficiency ;  that  is,  to  the  rela- 
tions or  apparatus  which  intervene  between  an  expenditure  and 
the  result  obtained,  rather  than  to  the  expenditure  and  result  them- 
selves. It  will  be  an  advantage  also  to  give  some  primary  consider- 
ation to  the  data  and  results.  For  instance,  it  is  often  an  aid  to 
efficiency  to  make  it  a  rule  to  strive  after  those  results  which  are 
most  inclusive  and  multiplicative  in  value  while  at  the  same  time 
making  the  data  employed  as  inexpensive  as  possible;  in  other 
words,  to  realize  that  the  efficiency  of  a  process  is  in  proportion  to 
the  gap  between  the  expenditure  and  the  result.  A  comprehensive 
review  of  the  various  aims  and  ends  of  processes  will  be  useful  as 
a  means  of  forming  even  an  approximate  scale  of  values  in  any 
situation.  Since  the  result  of  one  process  may  be  data  of  another 
process,  the  study  of  possible  expenditures  and  results  should  also 
facilitate  the  linking  of  such  processes  together  so  as  to  form  more 
or  less  comprehensive  systems  for  obtaining  desired  ends.  If  even 
a  rude  common  essence  of  values  could  be  obtained,  other  equally 
or  even  more  important  advantages  would  follow.  Accordingly  the 
expenditures  and  results  of  efficiency  processes  will  be  the  main 
object  of  investigation  in  the  present  chapter.  Primary  attention 
will  be  given  to  results  aimed  at,  expenditures  being  considered 
largely  by  implication. 

CLASSIFICATION 
Results  Grouped  according  to  Materials 

We  shall  first  classify  the  aims  and  results  of  efficiency  pro- 
cesses according  to  the  materials  of  which  they  are  constituted. 
Proceeding  thus  we  obtain  the  following  groups  of  aims : 

Physical  objects  or  forces,  including,  for  instance,  land,  buildings, 
mines,  tools,  machinery,  light,  heat,  mechanical  power,  speed,  and 
all  other  species  of  so-called  material  inorganic  wealth. 

152 


EXPENDITURES  AND  RESULTS  153 

Biological  results,  as  plants  and  animals  and  their  useful  products, 
as  food,  warmth,  shelter,  life,  offspring. 

Personal  or  psychological  results,  as  pleasure,  power,  health, 
leisure,  knowledge,  education,  comfort,  welfare,  well-being. 

Social  results,  as  position,  fame,  friendship,  love,  service;  social 
means  to  these  ends,  as  social  and  political  organization;  and  com- 
plexes of  these  results,  such  for  instance  as  are  included  under  a 
term  like  civilization. 

Ethical  and  religious  results,  as  character,  the  approval  of  one's 
conscience,  and  religious  conversion. 

Abstract  formal  results,  as  space,  time,  freedom,  reuse,  groups, 
and  the  various  categories  and  Efficients  both  as  means  to  ends,  and 
also,  from  certain  points  of  view,  as  ends  in  themselves.  In  the 
past  the  uniformity  or  equivalence  aims  which  come  under  this 
head,  such  as  peace,  truth,  and  reality,  have  been  unduly  empha- 
sized as  ultimate  ends,  though  perhaps  they  cannot  be  too  greatly 
emphasized  as  means  to  ends. 

Evidently  one  of  the  above  results  (especially  some  item  in  one 
of  the  later  classes)  often  includes  or  quickly  brings  others.  Thus 
good  government  often  means  wealth,  health,  education,  and  happi- 
ness to  many  citizens. 

Results  Grouped  according  to  Forms 

The  results  of  efficiency  processes  may  also  be  classified  with 
reference  to  their  form. 

Thus  with  respect  to  size  results  aimed  at  may  be  large  or  small ; 
one,  two,  three,  or  w-dimensional.  With  reference  to  other  spatial 
categories,  they  may  be  local  or  omnipresent;  may  have  various 
shapes;  may  occupy  different  positions,  as  when  they  are  internal 
or  external  to  data.  With  reference  to  number,  they  may  be  single 
or  manifold. 

In  this  connection  it  is  especially  important  to  observe  that  they 
may  be  direct  or  indirect.  Thus  adaptation  to  one's  environment  is 
not  so  much  an  end  in  itself  as  a  means  to  an  end.  From  our 
point  of  view,  as  has  already  been  remarked,  equivalence  results  (as 
truth,  reality,  accuracy,  justice)  are  not  ultimate,  but  proximate 
and  intermediate.  A  mere  means  to  a  result  often  becomes  of  such 
importance  that  it  comes  to  be  regarded  as  itself  a  more  or  less 
ultimate  end  of  action.     This  being  the  case,  from  certain  points 


154  SOURCES  OF  EFFICIENCY 

of  view  it  is  often  useful  to  sum  up  the  equivalence  and  more 
ultimate  ends  of  action  in  couplets  like  the  following:  light  and 
sweetness,  truth  and  love,  science  and  sentiment,  the  universe  as 
mechanism  and  the  universe  as  idea,  certitude  and  utility,  realism 
and  idealism. 

With  reference  to  time  results  may  be  temporary  or  permanent, 
and  may  come  quickly  or  slowly.  Similarly  they  may  be  reciprocal 
(with  the  data)  ;  positive  or  negative;  simple  or  complex.  Instances 
of  complex  results  are  all  the  beneficial  changes  included  in  a  case 
of  wholesome  growth,  as  for  instance  the  change  from  the  acorn 
to  the  oak,  or  the  results  of  civilization. 

The  beneficial  results  of  an  efficiency  process  may  occur  in  a 
grouped  or  multiplicatively  grouped  form.  An  illustration  of 
grouped  results  is  knowledge  as  including  health,  wealth,  fame, 
service,  and  happiness.  Often  in  this  connection  relativity  is  pres- 
ent. Thus  each  item  in  the  list  of  the  results  just  mentioned  may 
lead  to  or  include  the  others.  Thus  health  often  leads  to  knowl- 
edge, wealth,  happiness,  etc.  In  this  manner  groups  are  obtained 
which  may  be  regarded  as  sub-groups  in  a  larger  system. 

By-products 

A  somewhat  important  method  of  classifying  results  in  this  con- 
nection is  that  which  makes  a  distinction  between  direct  results  and 
by-products.  Thus  cattle  are  slaughtered  primarily  for  the  meat 
which  they  supply  as  food.  But  when  the  process  is  rightly  con- 
ducted a  host  of  by-products  is  also  obtained  such  as  hides,  oils, 
oleomargarine,  stearine,  tallow,  soap,  fertilizers,  medical  extracts, 
dye  stuffs,  buttons,  glue,  bone,  charcoal,  some  hundreds  in  all. 
The  externality  of  carrying  on  work  on  a  large  scale  often  makes 
by-products  particularly  important.  In  highly  competitive  work, 
the  by-products  may  become  the  chief  source  of  profit.  Much 
relativity  frequently  comes  into  play  in  determining  what  is  a  main 
and  what  a  by-product.  The  side  results  are  often  abstract  and 
scarcely  observed,  but  at  the  same  time  of  prime  importance.  Such 
for  instance  are  experience  gained,  particularly  knowledge  and 
power  concerning  efficiency  processes. 


EXPENDITURES  AND  RESULTS  155 

Scales  of  Results 

As  a  continuation  of  this  line  of  thought  it  follows  that  the  dis- 
tinction between  results  as  of  higher  or  lower  order  is  of  the  first 
importance.  A  graded  series  of  results  may  be  obtained  with  refer- 
ence to  various  categories.  Thus  with  reference  to  the  perpetuation 
of  the  race,  the  aims  and  ends  of  processes  in  the  order  of  their 
importance  are  self-preservation  (including  food,  shelter,  life)  ; 
self -propagation  (offspring)  ;  happiness;  self-sacrifice. 

The  matter  of  arranging  all  results  in  a  general  and  inclusive 
multiplicative  scale  will  be  considered  in  connection  with  the  analysis 
of  surplusages  as  a  whole  and  their  comprehensive  marginal  multi- 
plicative grouping. 

Before  taking  up  this  topic,  it  will  be  of  advantage  briefly  to 
analyze  certain  terms  which  are  often  used  to  express  the  results  of 
processes.  One  of  the  most  important  of  these  terms  is  the  word 
value. 

Value  and  Worth 

The  term  value  as  currently  used  has  two  widely  different  mean- 
ings, which  are  often  confused,  viz. :  ( i )  an  equivalence  meaning 
and  (2)  a  surplusage  meaning.  Thus  in  the  phrase  *'the  value  of  a 
gallon  of  oil"  the  first  or  equivalence  meaning  of  the  word  value  is 
the  amount  of  money  that  may  be  obtained  by  selling  the  oil  (i.e., 
money  value)  ;  or  the  amount  of  heat  generated  by  burning  the  oil 
(i.e.,  fuel  value)  ;  or  the  amount  of  coal  which  when  burned  will 
produce  the  same  amount  of  heat  as  the  oil  (i.e.,  coal  value). 

The  second  or  surplusage  meaning  of  the  words  is  the  superior- 
ity of  oil  with  respect  to  another  kind  of  fuel  (which  is  equivalent  in 
heat  value),  as  the  superiority  of  the  oil  in  concentration,  lightness, 
rapidity  of  combustion,  and  power  to  give  a  war  vessel  a  large  radius 
of  action  and  consequent  capacity  to  win  naval  battles.  In  like 
manner  it  may  have  meanings  of  these  two  kinds  in  other  ways 
and  in  comparison  with  other  substances,  for  instance  as  a  kind  of 
lubricant  or  an  insecticide,  or  as  a  source  of  coal  tar  and  its  pro- 
ducts, or  as  a  means  of  calming  stormy  waters  at  sea. 

In  this  book  the  term  value  is  used  as  far  as  possible  in  the 
second  or  surplusage  sense. 

The  term  worth  has  two  similarly  contrasted  meanings.     These 


156  SOURCES  OF  EFFICIENCY 

are  illustrated  in  the  sentences,  'This  house  is  worth  $2000",  and 
"Mr.  X.  is  a  man  of  great  worth". 

ANALYSIS  AND  MULTIPLICATIVE  GROUPING  OF  THE  AIMS 
OF  EFFICIENCY 

If  we  attempt  to  tabulate  the  aims  and  ends  of  efficiency  pro- 
cesses in  a  comprehensive,  hierarchical,  and  completely  filial  form 
by  the  customary  method  of  progressively  including  sub-aims  in 
larger  and  larger  aims,  we  are  hindered  by  the  complexity  and  cross 
relation  of  many  of  the  value  concepts  involved  and  by  their  quali- 
tative incommensurability.  However,  we  may  make  what  is,  in 
some  respects,  an  even  more  useful  systematization  of  the  aims  and 
ends  of  efficiency  processes  by  analyzing  efficiency  aims  into  a  scale 
of  constituent  elements  and,  by  use  of  these  elements,  building 
up  values  or  aims  into  a  marginal  multiplicative  group  system,  gen- 
eral and  undeveloped  in  some  respects,  but  serviceable  in  many 
more  or  less  fundamental  ways. 

Four  Elements  in  Valuable  Results 

The  first  and  most  fundamental  constituent  in  the  result  aimed 
at  in  any  efficiency  process  is  that  of  non-equivalence  with  respect 
to  the  datum  or  expenditure,  or  a  certain  disproportion  between 
means  and  ends.  This  non-equivalence  may  be  positive  or  negative, 
that  is,  may  represent  gain  or  loss.  It  may  be  quantitative  or  quali- 
tative. When  it  is  quantitative  it  may  be  named  a  surplusage. 
When  it  is  qualitative  (as  when  physical  exercise  produces  good 
health)  it  is  useful  to  realize  it  as  a  fact,  to  regard  certain  cases  of 
it  as  units  or  elements,  and  to  reuse,  group,  and  extend  them 
systematically. 

The  second  constituent  in  the  results  with  which  we  are  particu- 
larly concerned  is  a  certain  positive  or  plus  quality.  It  often  re- 
quires much  externality  to  determine  this,  yet  it  is  an  important 
source  of  efficiency  to  recognize  it  as  a  distinctive  element  in  results 
sought  after,  and  to  regard  it  in  its  most  fundamental  forms  as 
primarily  impersonal  or  subpersonal.  Thus  groups  as  such  and 
as  a  whole  have  values  and  uses  which  are  practically  universal  and 
only  occasionally  in  the  systematic  scheme  of  things  take  personal 
form. 


EXPENDITURES  AND  RESULTS  157 

The  third  principal  constituent  in  efficiency  results  is  that  suppHed 
by  the  element  of  personality  in  its  various  forms.  It  is  this  which, 
when  annexed  to  positive  non-equivalence,  causes  it  to  become 
happiness  or  well-being. 

The  fourth  class  of  constituents  are  those  more  or  less  concrete 
elements  which  when  annexed  cause  positive  non-equivalence  to 
take  such  special  forms  as  food,  or  offspring,  wealth,  or  fame;  or 
which  cause  personal  positive  non-equivalence  to  take  the  form  of 
special  sensations  of  pleasure  as  that  of  warmth,  or  some  form  of 
pleasure  which  is  related  to  any  special  organ  of  the  body  or  faculty 
of  the  mind. 

It  is  not  necessary  that  all  of  these  four  classes  of  constituents 
be  present  in  a  given  result.  Thus  if  a  process  produces  a  new 
and  better  system  (or  groupage)  only  the  first  two  constituents 
are  present  in  the  result  obtained.  In  a  sensing  of  beauty  or  sub- 
limity only  the  first  three  are  present. 

This  analysis  at  least  makes  possible  an  approximate  multiplica- 
tive group  system  of  values  in  any  given  situation  and  opens  the 
way  to  many  directive  and  other  efficiency  processes  in  the  treat- 
ment of  such  values. 

Illustrations  of  the  Four  Elements 

Specific  illustrations  will  aid  in  making  clear  the  meaning  and 
general  uses  of  the  above  analysis  and  the  multiplicative  group 
synthesis  thus  made  possible.  A  careful  examination  of  the  acts 
of  a  boy,  for  instance,  shows  that  the  dominant  source  of  pleasure 
in  a  boy's  nature  is  fundamentally  that  of  generating  or  obtaining 
a  surplus  as  such,  any  immediate  concrete  gain  to  himself  being 
a  secondary  matter.  Many  of  his  acts  of  mischief  are  performed 
not  because  he  delights  in  destructive  deeds  as  such,  but  because 
he  finds  his  greatest  pleasure  in  a  mere  disproportion  between 
means  employed  and  the  results  which  follow.  Hence  by  sufficiently 
tactful  treatment  he  may,  if  he  is  normal  in  body  and  mind,  almost 
always  be  led  to  conduct  which  will  give  this  same  sort  of  pleasure, 
but  will  also  be  profitable  in  other  ways  to  all  concerned.  For  a 
like  reason  a  child  is  often  more  interested  in  working  out  and 
operating  a  puzzle  which  has  no  concrete  use  than  by  making 
money  by  raising  crops  in  a  garden.    In  like  manner  the  able  busi- 


158   •  SOURCES  OF  EFFICIENCY 

ness  man  frequently  finds  more  pleasure  in  business  as  a  game, 
that  is  as  a  mere  means  of  obtaining  marvellous  results,  than  in  the 
yacht  or  paintings  which  financial  profits  enable  him  to  buy  and 
enjoy.  So,  also,  many  persons  read  the  newspapers  primarily  for 
the  new  sensations  which  they  thus  experience,  that  is  the  new 
pleasure  which  they  obtain  from  the  perception  of  new  and  strange 
diversities,  externalities,  and  groupages,  rather  than  from  the  direct 
concrete  utility  of  the  new  facts  which  are  assimilated.  The  dom- 
inant surplusage  principle  in  both  of  these  cases  is  sound  as  far  as  it 
goes  but  it  needs  careful  safeguarding  and  directive  treatment  in 
connection  with  the  other  constituents  of  efficiency  results. 

A  somewhat  higher  case  is  that  in  which  a  more  fundamental 
pleasure  is  found  in  harmony,  beauty,  and  sublimity,  or  in  living  a 
highly  moral  and  broadly  sympathetic  life  (that  is,  in  highly  de- 
veloped forms  of  groupage  and  externality)  than  in  food  or  money, 
which  indeed  are  often  mere  detailed  consequences  of  the  primal 
efficiency  principles  involved  in  the  former  cases. 

Advantages  in  the  Use  of  the  Four  Elements 

The  efficiency  advantages  which  flow  from  the  preceding  analysis 
and  systematization  of  values,  call  for  some  more  formal  and  ex- 
tended statement. 

In  the  first  place  it  is  to  be  noted  that  the  first  and  more  funda- 
mental and  therefore  comprehensive  constituents  in  values  (viz. : 
positive  non-equivalence  or  groupage)  are  practically  omnipresent 
and  in  a  vast  number  of  cases  may  be  had  at  little  or  no  cost ;  also 
that  by  obtaining  them  thus  the  more  specific  forms,  those  which 
are  usually  expensive  when  sought  for  individually,  may  be  obtained 
at  slight  cost  by  the  use  of  the  marginal  reuse.  Thus  every  occupa- 
tion, however  humble  in  its  conventional  rating,  as  cooking  or- 
boot-blacking  even,  is  saturated  in  many  ways  with  the  various 
Efficients  which  may  become  sources  of  the  highest  pleasure  when 
properly  understood.  For  all  persons  also  the  sight  of  a  sunset 
costs  nothing,  and  when  to  this  is  annexed  some  knowledge  of  the 
principles  of  esthetics  and  art  gained  from  books  or  art  galleries  at 
small  cost,  highly  specialized  forms  of  pleasure  and  value  are 
obtained  at  slight  expense.  By  pursuing  methods  Hke  these  the  way 
is  also  often  opened  for  the  attainments  of  results  more  or  less  in 
groups  instead  of  singly. 


EXPENDITURES  AND  RESULTS 


159 


It  follows  also  that  the  prime  source  and  method  of  social  ef- 
ficiency is  to  generate  or  create  positive  non-equivalence  constantly 
and  in  all  possible  ways  quite  regardless  of  all  personal  considera- 
tions, or  at  least  putting  all  such  considerations  in  a  secondary  place. 
New  light  is  thus  thrown  for  instance  on  ethical  principles.  For 
the  method  of  life  thus  indicated  includes  as  a  detail  the  doing  of 
good  to  those  who  have  annoyed  us.  At  one  stroke  it  eliminates 
revenge,  selfishness,  heartless  fun,  pessimism,  and  substitutes  some- 
thing better.  It  puts  constructive  work  and  plusness  in  all  forms 
in  the  foreground  actively  and  constantly.  Personal  considerations 
are  set  apart  but  are  always  within  hailing  distance.  It  makes  it 
possible  for  each  individual  to  enjoy  the  primal  essence  of  all 
things  not  only  without  interference  with  others  but  rather  by  pri- 
tnarily  aiding  others.  It  follows,  of  course,  that  this  view  makes 
one  expectant  of  and  ready  to  utilize  all  new  forms  and  kinds  of 
useful  results. 

Other  Advantages 

One  or  two  matters  of  detail  should  also  be  mentioned  in  this 
connection.  If  positive  non-equivalence  is  the  primal  essence  of 
values  it  follows  that  a  method,  at  least  approximate,  is  thus  sup- 
plied of  ranking  and  ordering  the  various  means  of  obtaining 
results  in  a  given  field  and  hence  of  accelerating  and  otherwise 
improving  the  attainment  of  these  results.  Thus  in  educational  work 
those  studies,  as  a  rule  will  be  most  valuable  which  give  the  greatest 
surplusage  and  groupage,  or  the  greatest  groupage  powers.  The 
same  remark  will  apply  to  other  callings  or  departments  of  life 
and  work. 

A  still  more  general  result  is  that  the  above  treatment  of  values 
gives  a  comprehensive,  sound,  and  vital  scheme  of  efficiency,  all 
parts  of  which  reinforce  each  other. 

Drawbacks  and  Their  Remedy 

At  the  same  time  mention  should  be  made  of  the  fact  that  the 
above  method  of  viewing  and  treating  the  results  aimed  at  in  ef- 
ficiency processes  has  certain  drawbacks.  One  of  these  is  a  fre- 
quent coldness  and  lack  of  force  due  to  the  absence  of  personality. 
Another  is  the  fact  that  putting  non-equivalence  (instead  of  some 


l6o  SOURCES  OF  EFFICIENCY 

form  of  uniformity)  in  the  first  place  may  open  the  way  under 
some  cases  to  incoherence  and  lack  of  system  as  when  each  person 
in  a  community  tries  to  form  his  own  system  of  values.  However, 
a  closer  view  of  the  matter  will  show  that  these  defects  are  largely 
superficial.  For  the  outgoing  power  inherent  in  the  multiplicative 
principle  will  be  in  the  end  remedy  the  first  of  these  defects  and  the 
corrective  power  which  is  also  inherent  in  the  multiplicative  princi- 
ple will  check  and  remedy  the  second. 

Advantages  Illustrated  by  Human  Progress 

As  a  general  illustration  of  the  advantages  to  be  gained  in  effi- 
ciency processes  by  making  subpersonal  positive  non-equivalence 
the  primary  and  most  fundamental  element  in  the  results  sought, 
it  may  be  well  to  point  out  that  during  the  last  five  hundred  years 
human  progress  in  general  has  largely  been  determined  by  the 
progress  of  science,  and  that  the  most  important  factor  in  the 
increase  of  scientific  knowledge  has  been  that  of  making  the  sub- 
personal  point  of  view  fundamental.  Thus  modern  chemistry 
arose  after  the  spirits  of  the  medieval  alchemist  had  bee«  discarded. 
The  astrologist  regarded  the  planets  as  animated  and  personal. 
Even  Kepler  viewed  the  earth  as  analogous  to  a  huge  animal,  and 
Newton  was  able  to  establish  the  law  of  gravitation  only  by  disen- 
tangling the  problem  from  all  immediate  considerations  of  personal- 
ity. On  the  other  hand  science  perhaps  has  erred  at  times  by  trying 
to  eliminate  the  category  of  personality  altogether,  instead  of 
putting  it,  at  least  for  the  time  being,  in  a  secondary  place.  That 
is,  it  has  reacted  too  far  from  the  medieval  point  of  view.  Appar- 
ently also  it  has  erred  frequently  by  exalting  mere  equivalence 
(or  "truth")  above  the  fruitful  results  of  equivalence,  that  is  above 
positive  non-equivalence  and  the  various  special  forms  which  this 
assumes.  Hence  the  results  obtained  by  the  scientific  method  in  the 
past  would  seem  to  be  but  an  imperfect  glimpse  of  those  obtainable 
by  a  broader  and  more  exact  view  of  efficiency. 

Relation  to  Chapter  I 

Before  concluding  the  present  chapter  it  will  be  well  to  consider 
briefly  its  relation  to  Chapter  I.  In  Chapter  I  the  main  discussion 
related  to  quantitative  homogeneous  efficiency.     Cases  of  hetero- 


EXPENDITURES  AND  RESULTS  i6l 

geneous  or  qualitative  efficiency  were  treated  only  by  the  ratio  or 
comparative  method.  In  the  present  chapter  the  intention  has  been 
to  treat  qualitative  efficiency  by  a  more  direct  method,  viz.:  by  a 
comprehensive  view  of  such  cases,  an  analysis  of  them  into  a  pro- 
gressive series  of  elements,  and  the  synthesis  of  them  into  a  more 
or  less  complete  multiplicative  group  system.  This  method  includes 
the  methods  of  Chapter  I  as  special  details  and  hence  gives  a  more 
comprehensive  and  aggressive  view  of  the  whole  matter  under 
consideration. 

Summary  and  Outlook 

The  substance  of  the  present  chapter  may  now  be  briefly  stated. 
The  study  of  the  aims  and  ends  of  efficiency  processes  is  important 
both  in  itself,  and  also  as  a  means  of  improving  these  processes. 
Aims  and  ends  may  be  classified  as  to  the  materials  composing 
them  (viz.,  as  mineral,  psychological,  social,  etc.)  ;  and  also  ac- 
cording to  their  form.  An  important  distinction  in  the  latter  respect 
is  that  between  the  main  result  and  a  by-product. 

Aims  and  ends  of  all  kinds  are  analyzable  into  four  principal 
elements,  viz.:  (i)  non-equivalence  (between  datum  and  result); 
(2)  a  positive  quality;  (3)  the  element  of  personal  application;  (4) 
all  other  constituents.  By  means  of  this  analysis  we  find  that,  with 
respect  to  efficiency  processes,  the  most  important  and  omnipresent 
constituent  is  positive  non-equivalence.  The  subpersonal  nature  of 
this  aim  enables  us  to  strive  to  create  and  utilize  values  in  an  un- 
limited variety  of  ways  and  with  great  freedom.  In  particular  it 
prevents  much  waste,  opens  the  way  to  the  utilization  of  many  com- 
paratively costless  sources  of  pleasure,  and  to  an  ordering  of  and 
grouping  of  values  in  cases  where  such  a  process  would  otherwise 
be  difficult  or  even  impossible.  It  also  gives  that  breadth  of  view 
without  which  the  highest  and  most  continuous  efficiency  processes 
are  impossible.  Hence  it  is  not  surprising,  that,  as  the  world  has  ad- 
vanced this  view  of  the  aims  and  ends  of  conduct  has  become  more 
and  more  prominent. 

In  the  present  chapter  and  those  which  precede  it  we  have  dis- 
cussed the  meaning  of  the  term  efficiency  the  principal  general 
methods  by  which  efficiency  may  be  obtained  or  increased,  and  the 
ends  and  aims  of  efficiency.     In  the  chapters  which  immediately 


i62  SOURCES  OF  EFFICIENCY 

follow  we  shall  investigate  certain  more  special  methods  of  obtaining 
results  than  those  considered  in  the  preceding  chapters.  The  first 
of  these  more  individual  efficiency  agencies  relates  to  man's  cognitive 
faculty.  Others  that  follow  are  related  more  particularly  to  his 
powers  of  volition  or  action. 


EXERCISE  9 

Give  an   example  of  each  of  the  following  classes  of  the   fruits  of  ef- 
ficiency processes: 

1.  Inorganic  material        6.  Imaginative  ii.  Spatial 

2.  Dynamic  7.  Moral  12.  Reciprocal 

3.  Biological  8.  Religious  13.  Negative 

4.  Emotional  9.  Social  14.  Indirect 

5.  Intellectual  10.  Temporal  15.  Grouped 

16.  Multipiicatively  grouped 

17.  Give  a  set  of  results  which  form  an  order  of  materials  series  as  to 
their  relative  importance. 

18.  State  the  different  beneficial  results  (including  efficiental  ones)  involved 
in  shelter. 

19.  In  wealth  20.  Knowledge  21.  Power  22.  Health 

23.  Give  a  case  where  a  means  to  an  end  has  become,  in  effect,  an  end 
in  itself. 

24.  Give  a  by-product  in  the  manufacture  of  butter.    Of  pig  iron. 

25.  Give  a  set  of  desirable  results  each  of  which,  in  some  respects,  includes 
the  others. 

26.  Name  some  of  the  by-products  which  accompany  the  manufacture  of 
kerosene  for  illuminating  purposes. 

27.  Name  the  by-products  of  some  other  process  with  which  you  are 
familiar. 

28.  Give  an  instance  where  a  by-product  has  become  more  important  than 
the  original  principal  product. 

29.  Give  an  instance  of  the  conversion  of  a  source  of  loss  into  a  source 
of  gain. 

30.  Explain  the  different  possible  meanings  of  the  word  value  in  the 
phrase,  "value  of  a  bushel  of  wheat". 

31.  Give  an  example  of  the  use  of  the  word  "worth"  both  in  an  equiva- 
lence and  in  a  surplusage  sense. 

32.  Why  is  it  that  a  man  who  receives,  at  the  end  of  a  year,  5  per  cent 
in  addition  to  his  principal,  is  often  regarded  as  receiving  an  equivalent  for 
his  investment;  a  man  who  receives  8  per  cent.,  as  making  an  efficient  use 
of  his  money;  and  a  man  who  tries  to  obtain  300  per  cent  (as  by  investing 
his  money  in  mining  stocks),  as  attempting  to  obtain  something  for  nothing. 

33.  Discuss  the  various  ways  in  which  pleasure  in  one's  work  is  a  source 
of  efficiency  and  give  illustrations. 


EXPENDITURES  AND  RESULTS  163 

34.  State  the  various  kinds  of  pleasure  which  a  carpenter  may  experience 
when  building  a  house.  Also  state  in  some  detail  the  efficiency  results  of 
such  pleasures. 

35.  Make  a  similar  statement  concerning  a  teacher  and  his  or  her  work. 
S6.  Discuss  some  of  the  various  devices  which  an  employer  may  use  in 

causing  his  workmen  to  take  pleasure  in  their  work. 

37.  Also  those  which  a  person  in  a  given  calling  can  use  in  developing  his 
own  interest  in  the  same. 

38.  Discuss  the  subject  of  attention  in  connection  with  efficiency. 

39.  Name  a  number  of  efficiental  sources  of  pleasure  which  are  widely 
present  and  cost  little  or  nothing. 

40.  Explain  the  distinction  between:  "value  in  use"  and  "value  in  ex- 
change", as  used  by  political  economists. 

41.  The  term  truth  has  come  to  include  both  equivalence  relations  and 
also  the  surplusage  fruits  of  such  relations.  State  certain  truths  and  also 
the  equivalence  and  surplusage  elements  in  each  of  these. 

42.  State  the  various  useful  results,  both  immediate  and  more  remote, 
which  may  be  the  outcome  of  a  successful  teacher's  work. 

43.  State  the  same  for  money  expended  in  improving  the  water  supply  of 
a  city. 

44.  Ascertain  what  is  meant  by  the  term  "epigenesis"  and  show  how  it 
illustrates  the  idea  of  surplusage. 

45.  Explain  what  is  meant  by  synthetic  judgments,  and  in  what  respect 
they  illustrate  the  principle  of  surplusage. 


CHAPTER  X 

SYMBOLISM 

Introductory  Illustrations 

When  a  merchant  in  Chicago  wishes  to  buy  goods  in  New  York, 
by  writing  a  letter  he  can  often  save  himself  the  expense  of  a 
journey  to  New  York.  Or,  going  a  step  farther  by  sending 
a  telegram  he  can  diminish  in  an  important  degree  the  time  required 
for  obtaining  the  goods.  This  latter  advantage  often  leads  to  other 
advantages,  such  as  the  rapid  reuse  of  capital  or  the  making  of  a 
sale  that  would  otherwise  be  lost.  When  a  scientific  investigator 
makes  a  discovery,  by  publishing  the  fact  in  a  journal  he  opens  the 
way  to  its  immediate  and  wide  reuse.  Also  he  often  finds  that  in 
the  process  of  stating  his  discovery  in  terms  of  concepts  in  general 
use,  he  develops  and  extends  the  new  fact  or  principle.  When  a 
surveyor  enters  in  his  notebook  a  drawing  of  the  route  surveyed 
and  also  numerical  and  descriptive  facts  relating  to  it,  he  prevents 
mistakes  which  he  might  make  if  he  trusted  to  mere  memory,  fre- 
quently saves  himself  the  labor  of  making  a  resurvey,  and  also 
puts  the  facts  obtained  in  such  a  form  that  they  can  readily  be 
grouped  in  various  forms  and  made  the  basis  of  efficient  action  by 
himself  and  others  in  different  ways,  as  in  building  a  railroad. 

The  above  instances  illustrate  the  fact  that  the  use  of  symbols  may 
be  an  important  aid  in  obtaining  useful  results.  Accordingly  sym- 
bolism is  the  next  primary  agent  of  efficiency  which  we  shall  study. 

CLASSIFICATION 

Cases  of  symbolisms  might  be  grouped  and  named  according  to 
the  objects  or  materials  represented  by  the  given  symbols,  but  such 
a  classification  is  not  important  for  our  purpose.  It  is  well  t<.» 
observe  however  that  any  object  or  entity  may  be  denoted  by  a  sym- 
bol and  usually  by  many  different  kinds  of  symbols.  Extreme  but 
important  cases  are  the  representation  of  nothing  (absence  of 
material)  by  some  sign,  as  the  absence  of  a  number  by  the  zero  mark ; 
or  of  an  unknown  object  or  number  by  a  sign,  as  x;  or  of  a  partially 
known  object  by  a  symbol,  as  in  certain  cases  in  chemistry. 

164 


SYMBOLISM  '  165 

Objects  Usable  as  Symbols 

More  valuable  for  our  purpose  is  the  classification  of  symbolisms 
according  to  the  material  of  which  they  are  composed. 

In  the  first  place  we  find  many  material  inorganic  objects  employed 
in  whole  or  part  as  signs  or  marks.  Examples  are  dress,  flags,  ink, 
paper,  pencil  marks,  paint,  idols  made  of  stone,  certain  fetishes, 
incense,  clouds,  the  wind,  the  ocean,  the  barometer,  thermometer, 
etc.  Such  symbolisms  are  further  illustrated  by  quotations  like  the 
following:    "He  is  pure  gold",  or  "He  is  a  star". 

Also  a  physical  force,  as  gravitation  or  electricity,  may  be  used  as 
an  expressive  representation  of  some  other  kind  of  power.  Thus 
we  speak  of  a  weighty  idea,  of  a  magnetic  person,  or  say  that  a 
man  is  a  live  wire. 

Of  especial  importance  in  this  connection  are  light,  color,  and 
sound.  Examples  of  the  employment  of  light  and  color  in  symbol 
form  are  the  black  and  white  of  the  printed  page,  color  as  it  appears 
in  paintings,  flowers,  the  warning  colors  of  animals,  and  certain 
signals  in  railroading.  Color  often  has  abstract  and  conventional 
meanings.  An  instance  in  the  use  in  art  of  red  and  green  to  denote 
the  concrete,  and  of  blue  to  express  the  abstract. 

Among  the  sounds  which  are  recognized  or  used  as  symbols  are 
thunder  and  various  other  sounds  made  by  inorganic  objects,  the 
sounds  made  by  birds  and  other  animals,  the  cry  of  a  baby,  the  yell 
of  a  savage,  the  drum  signals  of  the  African,  spoken  articulate 
language,  and  an  organization  of  sounds  such  as  is  found  in  a 
symphony  or  fugue. 

A  living  object  or  a  combination  of  living  objects  may  often  form 
a  useful  symbol.  Thus  green  grass  denotes  the  presence  of  water, 
and  a  buzzard  the  proximity  of  carrion.  Living  objects  are  used 
as  symbols  in  a  more  abstract  way,  as  when  we  say,  for  example, 
that  a  certain  man  is  a  lion  or  an  eagle. 

In  like  manner  it  is  often  advantageous  to  use  a  part  of  a 
living  object  as  a  symbol  for  the  wh©le  object.  Examples  are  the 
recognition  of  a  plant  by  means  of  its  leaves  or  flowers,  or  an 
elephant  by  his  trunk.  So  a  beard  is  sometimes  a  convenient  symbol 
for  a  man,  and  a  criminal  may  be  identified  by  the  marks  on  his 
finger  tips.    So  a  smile  or  a  gesture  may  express  a  state  of  mind. 

Similarly  a  mind,  or  a  mental  state,  attribute,  or  product  frequently 


l66  SOURCES  OF  EFFICIENCY 

forms  an  eflfective  symbol.  Thus  a  feeling  of  pain  often  represents 
danger  or  loss ;  and  a  certain  feeling  of  pleasure  indicates  gain  or 
advantage. 

Certain  sensations  are  in  some  way  representative  of  the  outside 
world  and  must  be  interpreted  as  such.  Thus  some  sensations  of 
taste  or  smell  indicate  foods,  and  others  represent  poisons. 

So  certain  acts  symbolize  certain  degrees  of  knowledge  or  states 
of  feeling.  Also  a  mental  peculiarity  may  represent  the  past  educa- 
tion of  a  person,  or  his  early  environment,  or,  in  a  measure,  his 
parentage. 

An  entire  personality  may  also  be  a  symbol  as  when  an  ambassa- 
dor represents  a  nation.  In  certain  cases  a  personality  may  repre- 
sent more  or  less  impersonal  data.  Instances  are  the  use  of  a 
personal  concept  like  angels,  devils,  demons,  gods,  to  represent 
a  natural  force. 

Spatial  Objects  as  S3mabols 

The  different  spatial  categories  furnish  material  for  symbols  in 
various  ways.  For  example  a  group  of  points  is  frequently  used 
to  represent  a  set  of  objects  of  any  given  kind.  Or  one  point  may 
stand  for  a  number  of  points  or  objects.  Such  a  point  is  often 
termed  a  focus.  The  Braille  printed  alphabet  for  the  blind  consists 
entirely  of  aggregates  of  points.  So  a  line  may  be  made  to  stand  for 
an  object  in  various  useful  ways,  or  for  a  motion,  a  velocity,  dura- 
tion, relation,  etc.  Specific  illustrations  are  supplied  by  various 
diagrams  used  in  scientific  works.  Similarly  we  have  lines  of  force 
and  lines  of  cleavage.  The  bounding  Hues  of  an  area,  as  of  a 
country,  frequently  form  a  useful  symbol  for  the  whole  area. 
Similarly  a  solid  object  may  be  denoted  by  its  bounding  lines. 
The  letters  used  in  writing  and  printing  are  made  up  essentially  of 
lines.  Punctuation  marks  are  points  and  small  lines  which  indicate 
to  the  eye  the  main  parts  of  the  group  structure  of  a  sentence. 

An  area  may  represent  the  product  of  any  two  factors.  Thus 
the  distance  passed  over  by  a  moving  body  may  be  represented 
by  an  area,  in  which  one  dimension  stands  for  the  time  occupied 
by  the  motion  and  the  other  dimension  represents  the  velocity  of  the 
moving  body.  In  common  life  and  perception  the  visual  surface 
of  a  physical  object  is  used  in  countless  ways  as  a  representative  of 


SYMBOLISM  167 

the  whole  solid  object.  Similarly  a  volume  may  be  used  to  stand 
for  the  product  of  any  three  factors.  Thus  interest  on  money  may 
be  represented  by  a  volume  whose  three  dimensions  are  principal, 
rate,  and  time.  Also  in  a  less  definite  way  volume  or  size  is 
employed  to  express  power,  influence,  or  efficiency  in  any  form.  So 
a  part  of  a  geometric  object  is  often  used  to  represent  the  whole. 

Shape  or  form  may  have  an  almost  innumerable  number  of 
different  symbolic  meanings.  The  closely  allied  category  of  posi- 
tion also  has  many  symbolical  uses.  For  instance  superiority  in 
power  or  influence  is  often  represented  by  a  higher  position  of 
some  kind,  as  a  seat  on  a  platform  in  a  public  meeting.  In  music 
gradations  in  pitch  are  indicated  by  a  series  of  positions  on  a  printed 
scale ;  also  simultaneity  of  sound  is  denoted  by  placing  on  the  same 
vertical  line  the  marks  which  represent  the  given  sounds.  Position 
is  also  used  as  a  principle  of  symbolism  in  other  highly  conventional 
but  important  ways,  as  in  the  arrangement  of  words  in  a  sentence,  of 
digits  in  a  number  such  as  78562,  or  of  symbols  in  various  combina- 
tions of  which  the  following  are  illustrations,  5^,  52,  25,  2^,  25. 

Neighborhood  Symbolism 

The  important  case  where  the  meaning  of  a  symbol  is  largely 
determined  by  its  surroundings  we  shall  name  neighborhood  sym- 
bolism. Thus  in  78562  the  meaning  or  value  of  the  7  depends 
mainly  on  the  number  of  symbols  which  follow  it.  A  similar  case 
is  that  of  a  word  like  bill  which  may  have  a  number  of  distinct 
meanings  and  whose  particular  meaning  is  determined  in  any  given 
case  by  the  context,  that  is,  by  the  position  of  the  given  word  with 
reference  to  adjacent  words.  As  an  illustration  we  may  take  the 
word  bill  in  the  two  sentences.  The  woodcock  has  a  long  bill ;  and, 
I  will  not  pay  this  bill. 

Other  Abstract  Symbols 

Number  is  used  as  a  symbol  in  many  ways.  Thus  it  may  express 
volume,  size,  position,  power,  or  efficiency  of  any  kind.  An  example 
of  the  latter  kind  is  contained  in  the  statement.  An  opportunity  in 
early  life  is  not  one  but  a  thousand. 

Similarly  time  and  its  various  categories  often  constitute  useful 
symbols.    Thus  time  may  represent  space  as  when  we  say  that  two 


l6B  SOURCES  OF  EFFICIENCY 

cities  are  eight  hours  apart.  Time  may  also  represent  growth, 
for  instance  a  person's  age  indicates  on  the  average  a  certain  stage  of 
development.  A  more  complex  case  is  the  use  of  time  as  representa- 
tive of  various  forces  operating  in  time,  as  when  we  say  that  time 
cures  all  ills. 

Motion  is  a  useful  symbol  in  a  variety  of  ways.  The  motion  of 
a  cloud  indicates  the  direction  and  velocity  of  the  wind  in  the 
stratum  of  air  which  contains  the  cloud.  The  flight  of  a  person  is 
often  a  sign  of  guilt  or  of  fright.  Certain  kinds  of  motion  indicate 
the  presence  of  life.  The  motions  of  a  workman  are  expressive  of 
the  amount  of  bodily  energy  he  is  expending. 

Motion  symbolism  may  take  an  elaborate,  articulate  form.  Ex- 
amples are  wigwagging  as  practised  in  the  signal  service  of  an 
army,  various  kinds  of  dancing,  finger  reckoning,  and  the  various 
forms  of  deaf  and  dumb  gesture  language. 

The  order  in  which  one  well  known  set  of  objects  is  customarily 
arranged  often  constitutes  a  simple  and  effective  means  of  indicating 
the  order  which  holds  among  a  less  familiar  set.  Thus  on  a  geo- 
logical map  the  order  in  time  of  the  geological  strata  is  often  con- 
veniently denoted  by  the  order  of  the  colors  of  the  spectrum.  Simi- 
larly on  a  topographical  map  the  parts  of  the  ocean  are  frequently 
denoted  by  blue,  lands  little  above  the  sea  level  by  green,  and  moun- 
tains by  red,  the  various  intermediate  colors  and  shades  of  the 
spectrum  being  used  to  express  various  intermediate  degrees  of 
elevation  of  the  land  surface.  In  like  manner  the  order  of  letters 
in  the  alphabet,  and  of  numbers  in  the  number  scale  are  frequently 
used  as  symbols  for  other  cases  of  order,  as  of  order  in  a  multiplica- 
tive series  scale. 

Efficients  as  Sjonbols 

Entities  of  a  still  more  abstract  and  general  kind  may  be  employed 
as  symbols.  In  general,  any  Efficient,  or  any  part  of  an  Efficient, 
may  be  used  as  a  brief  and  comprehensive  symbol  of  other  things. 
Thus  an  element  may  represent  a  group,  or  one  group  may  stand  for 
any  other  group  or  form  of  groupism.  Any  diversity  may  be  repre- 
sented by  a  diversity  of  any  other  sort  as  by  an  irregular  mark  like 
<  or  ' — '.  So  we  often  represent  any  uniformity  by  any  other  more 
convenient  or  powerful  uniformity.    An  important  case,  already  re- 


SYMBOLISM  169 

ferred  to  in  different  places  is  that  in  which  an  equivalence  of  some 
particular  kind  stands  for  ubiquitous  available  surplusage,  as  when 
peace  is  used  as  a  symbol  for  constant  potential  happiness.  So  any 
instrument  may  be  a  symbol  for  the  fruits  of  that  instrument. 

Absence  as  a  Symbol 

An  extreme  case  of  efficiency  in  symbols  is  that  in  which  mere 
absence  of  anything  represents  some  particular  object  or  entity. 
Thus  empty  space  may  be  a  sign  for  some  number  agreed  upon; 
X  when  used  for  \x^  is  a  twofold  illustration  of  this  principle. 
Absence  or  silence  may  indicate  dislike,  forgetfulness,  suspicion,  or 
have  any  prearranged  meaning.  Thus  we  have  the  saying  "Silence  is 
more  eloquent  than  words."  A  convenient  and  widely  applicable 
symbolism  of  this  sort  is  the  representation  of  the  absence  of 
obstacles  and  the  resulting  speed  or  power  by  a  vacuum.  Thus  a 
railroad  system  may  be  conceived  of  as  a  branching  vacuum  con- 
necting important  places  which  are  stores  and  sources  of  positive 
surplusage. 

S3rmbols  Formed  of  Complex  Materials 

Evidently  the  above  materials  out  of  which  symbols  are  formed 
may  be  compounded  and  complexed  in  many  ways.  An  illustration 
is  the  combination  of  symptoms  in  the  human  body  which  indicates 
health  or  the  presence  of  some  particular  disease.  This  combina- 
tion may  consist  of  a  coating  on  the  tongue,  feelings  of  pain  or 
pleasure,  sounds  of  different  kinds,  lines  in  the  face,  color  of  the 
complexion,  temperature,  position  of  the  bodily  parts,  action  of  the 
pulse  or  heart,  absence  of  appetite,  changes  of  growth  or  decay. 

Symbols  Classified  according  to  Forms 

It  is  often  also  an  advantage  to  characterize  certain  symbolisms 
according  to  their  forms  or  some  other  prominent  quality. 

Thus  with  respect  to  personality  and  directive  processes  it  is 
often  useful  to  discriminate  between  symbols  which  have  been  de- 
vised by  a  person  for  his  own  use  {private  or  subjective  symbol- 
isms), and  those  which  are  objective  and  general. 

In  a  still  more  general  way  we  can  distinguish  symbols  which 
are  artificial  like  the  alphabet  and  those  which  are  natural  like  the 
colors  of  a  bird  or  the  beard  of  a  man. 


I70  SOURCES  OF  EFFICIENCY 

Spatial  and  Like  Forms 

A  spatial  element  is  often  prominent  in  a  symbolism.  In  particu- 
lar, it  is  useful  to  note  that,  from  the  relative  point  of  view,  a  dia- 
gram (or  other  symbol)  may  be  larger  than  the  material  represented, 
as  in  diagrams  of  molecular  structure,  or  smaller,  as  in  most  maps, 
printed  language,  etc. 

A  symbol  or  symbolism  may  be  of  one,  two,  three,  or  no  dimen- 
sions, examples  of  the  last  species  being  the  use  of  a  point  or 
empty  space  as  a  sign  of  something.  An  important  special  dimen- 
sional case  is  what  may  be  termed  the  semilinear  form  of  symbolism. 
This  consists  of  a  set  of  symbols  dominantly  linear  but  with  some 
width  varying  according  to  circumstances.  As  examples,  we  have 
a  line  of  print,  or  mathematical  symbols,  or  the  symbolisms  which 
are  found  in  a  person's  stream  of  consciousness. 

As  to  time  and  allied  categories,  various  symbolisms  may  be 
characterized  as  temporary  (provisional),  permanent,  survivals, 
prehistoric,  prenatal,  or  hereditary. 

With  reference  to  the  category  of  number,  the  specific  char^ 
acter  of  a  symbolism  miay  be  determined  in  several  different  ways. 
For  example  the  number  of  its  fundamental  symbols  is  often  an 
important  distinguishing  characteristic  of  a  given  system.  Thus 
the  Arabic  system  of  notation  for  numbers  contains  ten  symbols. 
This  numerical  element  in  a  symbolism  varies  greatly  owing  to  the 
fact  that  in  certain  cases  greater  efficiency  is  obtained  by  using 
only  a  few  primary  symbols,  and  in  other  cases  by  using  many. 

Manifold  Symbolisms 

Also  we  may  obtain  what  we  may  term  a  dual,  triple,  or  w-fold 
symbolism  by  symbolizing  a  given  domain  of  material  in  two,  three,, 
or  w-different  ways.  In  a  mine  a  danger  signal  often  consists 
both  of  the  ringing  of  a  bell  and  of  the  flashing  of  a  light  of  some 
kind.  The  policemen  of  a  city  are  denoted  by  their  names,  by  their 
numbers,  and  as  a  whole  by  their  uniforms.  A  country  may  be 
described  in  common  language,  or  by  maps,  or  diagrams,  or  tables 
of  numerical  data,  or  a  series  of  pictures,  each  method  having  its 
own  special  uses,  and  all  combining  multiplicatively  to  produce 
expressiveness  of  a  high  order. 

A  reciprocal  symbolism  is  a  combination  of  two  objects  or  of  two 
domains  of  material  such  that  each  may  be  used  as  a  symbolical 
representative  of  the  other.  An  example  is  furnished  by  the  music 
and  words  of  a  good  song. 


SYMBOLISM  171 

Symbolisms  Characterized  by  an  Efficient 

An  important  class  of  symbolisms  with  respect  to  the  category  of 
force  are  the  records  automatically  made  by  certain  machines. 

A  species  of  symbolism  is  often  best  characterized  by  that  Effi- 
cient which  is  most  prominent  in  its  form  or  structure.  Thus  it  is 
frequently  best  to  regard  a  case  where  the  whole  is  represented  by 
a  part  as  a  unit  and  multiplier  symbolism.  A  special  instance  of  this 
form  is  a  prize  of  any  kind  given  as  a  representative  or  specimen 
of  other  larger  rewards  to  come  later. 

Similarly  certain  important  species  of  symbolisms  have  a  marginal 
reuse  form.  Thus  a  conductor  on  a  railroad  train  instead  of  re- 
cording by  pencil  the  fact  that  a  certain  passenger  has  paid  his  fare 
saves  time  and  labor  by  simply  making  a  hole  in  the  passenger's 
ticket. 

A  symbol  may  be  systematically  grouped  in  its  inner  structure; 
and  in  like  manner  individual  symbols  or  symbolisms  may  be  com- 
bined so  as  to  form  a  multiplicatively  grouped  aggregate.  The  fact 
that  a  sentence  as  used  in  ordinary  language  is  essentially  a  multi- 
plicative group  structure  is  indicated  by  the  term  "articulate 
language". 

Orders  of  Symbolisms 

One  symbol  may  often  be  represented  by  another  and  frequently 
briefer  and  more  efficient  symbol ;  hence  symbolisms  may  be  of  dif- 
ferent orders.  Thus  ordinary  language  may  be  converted  into  short- 
hand (as  used  by  a  stenographer  in  reporting  a  speech),  or  stated 
in  terms  of  the  Morse  telegraphic  code,  or  expressed  in  some  species 
of  cryptography.  Hence  all  of  these  devised  systems  are  of  the 
second  order.  When  a  telegrapher  reads  a  message  by  sound,  the 
set  of  sounds  utilized  by  him  constitutes  a  symbolic  system  of  the 
third  order. 

One  symbol  may  also  be  of  higher  order  than  another  owing  to 
its  aggregate  superior  efficiency.  Thus  among  civilized  peoples,  a 
word  like  Jehovah  is  superior  in  significance  to  a  wooden  image  in 
representing  a  divine  principle. 

Scale  of  Departure  from  Appearances 

The  classification  of  symbols  (or  symbolisms)  according  to  the 
degree  of  their  departure  from  the  object  represented,  is  of  funda- 


172  SOURCES  OF  EFFICIENCY 

mental  importance.    In  this  respect  we  have  the  following  principal 
types : 

(i)  Cases  where  such  departure  is  slight,  as  in  photographs, 
maps,  geometric  outlines,  or  in  verbal  contractions,  as  the  use  of 
U.  S.  for  United  States.  In  such  symbols  the  transformations  in- 
volved consist  essentially  in  a  reduction  of  size,  or  a  syncopation 
(or  in  some  cases  of  an  expansion)  of  the  object  represented.  Often 
also  a  slight  reluctant  departure  from  the  form  of  this  object  is 
involved.  The  largest  departure  from  phenomenal  appearance 
allowable  in  this  respect  is  found,  perhaps,  in  the  representation  of 
a  solid  object  by  a  drawing  on  a  flat  surface. 

(2)  Diagrams  in  which  there  is  not  only  a  change  in  size,  but 
also  a  considerable  change  in  form,  as  in  a  diagram  of  the  human 
heart  with  the  parts  rearranged  so  that  the  process  of  the  heart's 
action  can  be  studied  in  consecutive  detail.  Similar  cases  are  a 
diagram  of  the  structure  of  a  molecule,  or  of  the  parts  of  a  sentence. 

(3)  Symbols  in  which  the  departure  from  the  form  of  the  object 
represented  is  preferential  and  aggressive.  Instances  are  the  word 
"man"  as  compared  with  what  the  symbol  represents;  the  use  of  x 
to  denote  the  volume  of  a  box ;  and  the  sign  =  instead  of  the  word 
"equals".  All  ordinary  verbal  language,  whether  spoken  or  written, 
shorthand,  telegraphic  codes,  etc.,  are  of  this  class.  In  this  connec- 
tion, special  mention  may  be  made  of  symbols  which  involve  an  un- 
limited or  infinite  departure  from  so-called  reality.  Examples  are 
the  representation  of  infinity  by  the  sign  00  and  zero  by  o.  So 
certain  religious  teachers  have  enforced  the  inferiority  of  matter 
and  evil  by  declaring  them  to  be  non-existent. 

Transcendent  Symbols 

Symbols  often  appear  in  a  more  or  less  unanalyzable,  mysterious, 
and  even  transcendental  form.  An  instance  is  the  combination  of 
marks  on  a  plant  by  recognizing  which,  even  before  blossoms  have 
been  produced,  a  plant  breeder  like  Luther  Burbank  is  able  to 
select  from  10,000  individual  plants  of  a  given  variety  the  two  or 
three  which  will  develop  specified  desirable  qualities.  Certain  physi- 
cians have  like  powers  in  reading  symptoms  of  diseases,  and  certain 
other  persons  in  reading  minds  and  characters.  Often  a  work  of  art, 
as  a  painting  by  Turner,  is  a  complex  and  a  more  or  less  transcenden- 
tal symbol. 


SYMBOLISM  173 

Complex  Forms  of  Symbolism 

It  is  evident  that  the  above  forms  may  be  compounded  and 
complexed  together  in  various  ways.  An  instance  is  found  in  a 
scientific  book  which  contains  not  only  ordinary  language  but  also 
mathematical  or  logical  formulas,  pictures,  diagrams,  and  numerical 
tables.  Its  statements  and  formulas  often  also  contain  implicit 
expressions  of  truths  and  facts  not  yet  fully  unravelled  and  perhaps 
beyond  our  full  comprehension. 

Two  General  T3^es  of  Symbols 

Before  closing  the  discussion  of  species  of  symbolisms,  it  will 
be  well  to  note  that  it  is  often  useful  to  group  different  kinds  of 
symbolism  into  two  main  classes  as  follows : 

I.  Geometric,  graphic,  or  pictorial  symbols.  These  are  preferentially 
single  (or  integral),  concrete,  depart  reluctantly  from  appearances 
and  appeal  primarily  to  the  sense  of  vision.  They  are  characterized 
by  vividness,  immediacy,  and  force  of  action. 

II.  Algebraic  symbols.  These  are  characterized  by  an  aggressive 
departure  from  appearances,  are,  in  general,  abstract  in  nature,  and 
composed  of  numerous  small  parts  which  are  combined  in  multipli-^ 
cative  group  fashion.  They  are  related  to  the  hand  and  higher 
mental  faculties  as  well  as  to  the  eye.  They  are  marked  by  their 
comprehensive  grasp,  ease  of  formation,  and  many-sided  efficiency. 

These  two  general  classes  of  symbols  may  also  be  briefly  de- 
scribed as  direct,  and  indirect. 

EfHciental  Essences 

An  important  form  of  the  first  of  these  two  classes  is  what  may 
be  termed  the  efficiental  essence  of  an  object  or  domain.  By  this  is 
meant  the  Efficients  which  together  form  the  dominating  structure 
of  the  object,  or  to  which  it  can  be  reduced,  and  which  often  can 
advantageously  be  used  in  place  of  the  object  or  domain.  A  simple 
example  is  the  set  of  lines  which  is  often  used  to  represent  a  box. 
Another  is  the  group  of  fundamental  ideas  which  form  the  essence 
of  a  book.  A  more  complex  case  is  the  aggregate  of  special  efficiental 
methods  which  characterize  any  particular  nation,  as  the  English,  or 
which  may  be  regarded  as  representing  a  given  type  of  civilization. 


174  SOURCES  OF  EFFICIENCY 

EFFICIENCY   FUNCTIONS   OF   SYMBOLS 

The  efficiency  functions  of  symbolism  are  presented  to  best  ad- 
vantage by  stating  them  in  terms  of  other  leading  principles  of 
efficiency. 

Symbols  a  Means  of  Economy 

Thus  many  of  the  advantages  connected  with  the  use  of  symbols 
appear  in  the  form  of  economies  or  groups.  For  instance  a  symbol 
usually  contains  far  less  material  than  the  object  represented.  A 
hundred  dollar  bill  weighs  much  less  than  one  hundred  gold  dollars 
and  still  greater  is  the  disparity  between  the  bill  and  one  hundred 
bushels  of  wheat.  Economy  of  this  kind  is  often  practically  infinite, 
as  when  a  house  is  represented  by  certain  diagrams,  or  by  the  word 
"house". 

Closely  connected  with  economy  of  material  is  economy  of  force 
or  energy.  For  example  it  is  much  easier  to  transfer  to  a  distant 
place  a  picture  of  a  house  than  the  house  itself. 

This  economy  often  takes  a  wide  and  complex  form.  An  illus- 
tration is  the  saving  of  energy  involved  in  reading  a  book  of  travels, 
instead  of  making  the  actual  journeys  described  in  the  book. 

Closely  connected  with  economy  of  material  and  energy  is  economy 
of  time  and  all  that  time  represents.  In  fact  the  proper  use  of  sym- 
bols may  beget  an  economy  in  each  and  every  element  employed  in 
producing  results.  These  economies  are  often  combined  in  complex 
forms.  For  example  the  colored  petals  of  a  flower  form  a  sign  to 
the  bee,  which  leads  to  a  saving  of  pollen  in  cross  fertilization, 
hence  to  a  saving  of  energy  to  the  plant,  and  to  a  saving  of  time  in 
the  evolution  of  the  plant  into  a  higher  form. 

An  Aid  in  Foming  and  Using  Groups 

Symbolisms  are  also  a  means  of  producing  more  positive  inclusions 
or  groups  than  economy.  Thus  the  symbols  which  represent  objects 
can  often  be  collected  into  a  small  portion  of  space  or  time  wherQ 
it  would  be  impossible  to  collect  the  objects  themselves.  An  example 
is  the  summation  in  figures  of  the  coal  deposits  of  the  United  States 
as  compared  with  a  physical  combination  of  all  this  coal  in  one  heap. 
Signs  and  signals  also  lead  to  concentrations  of  strength  and  action, 
as  in  games,  or  war,  business,  or  governmental  processes. 


SYMBOLISM  175 

A  Means  to  Reuse 

The  employment  of  symbols  often  leads  to  reuse  on  a  large  scale. 
A  printed  description  or  picture  of  a  building  often  produces  exten- 
sive multuse  of  the  principles  embodied  in  the  building.  If  it  were 
not  for  oral  or  printed  language  or  pictorial  representations  of  an 
object,  only  those  actually  witnessing  an  event  would  ever  know  of  it. 

This  useful  function  of  symbols  is  increased  by  the  ease  with 
which  they  can  be  preserved  on  account  of  their  conciseness.  This 
quality  makes  it  possible  readily  to  inscribe  them  on  lasting  materials 
or  to  shelter  them.  Symbols  lead  to  reuse  not  only  in  these  ways 
but  also  because  they  facilitate  the  action  of  the  imagination  and 
reason. 

When  we  say  that  a  certain  orator  is  a  star,  we  employ  reuse  of 
still  another  kind.  In  this  case  the  reuse  involved  is  that  of  work 
done  in  assimilating  the  meaning  of  a  star.  This  gain  also  takes  the 
form  of  added  force  and  vividness  in  the  process  of  communicating 
ideas. 

Ssrmbols  Auxiliary  to  Multiplicative  Group  Systems 

The  use  of  symbols  often  facilitates  the  formation  of  multipli- 
cative group  systems.  An  example  is  the  organization  of  an  army 
by  the  aid  of  uniforms,  and  various  flags  and  standards.  So  widely 
separated  objects  may  often  be  grouped  multiplicatively  by 
affixing  proper  tags  or  marks  to  them.  Many  systems  of  biologi- 
cal classification  are  obtained  essentially  in  this  way.  An  important 
illustration  from  the  business  world  is  the  coordination  of  several 
lines  of  work  in  a  machine  shop  or  other  establishment  by  means 
of  carefully  prepared  charts.  This  process  often  in  effect  consti- 
tutes the  combination  of  several  linear  group  systems  into  a  com- 
prehensive areal  one.  Similarly  the  tabulation  of  the  results  of  any 
large  and  many-sided  investigation  facilitates  the  discovery  of  laws 
governing  these  results,  and  the  use  of  checks,  tests,  and  various 
cross  multiplicative  groupings.  Also  the  multiplicative  grouping 
of  a  given  domain  of  material  in  terms  of  a  certain  few  units  taken 
as  fundamental  is  facilitated  by  expressing  these  units  in  symbolic 
form.  Thus  as  soon  as  a  national  consciousness  has  adopted  certain 
ideas  as  standard  or  primal  and  expressed  these  in  words,  other 
experiences  and  ideas  will  be  expressed  in  terms  of  these  standard 
ones,  and  the  national  life  will  be  correspondingly  systematized. 


176  SOURCES  OF  EFFICIENCY 

An  Aid  to  Other  Efficients 

In  like  manner  the  employment  of  symbols  develops  orders  of 
material.  Thus  in  business  processes  the  construction  of  efficiency 
curves  and  charts  facilitates  the  working  back  to  causes  and  sources 
of  efficiency  or  waste  and  the  formation  of  improved  processes  of 
work.  In  some  cases,  the  symbolism  itself  acts  as  a  higher  grade 
of  material  with  reference  to  the  objects  represented. 

In  the  use  of  symbols,  uniformities  are  developed  by  the  inten- 
tional making  of  different  symbols  of  the  same  general  size,  by  the 
reuse  of  symbols,  by  the  discovery  of  like  efficiental  essences  in 
different  domains,  or  by  the  permanence  conferred  on  the  data 
represented.  Symbols  also  furnish  diversities  in  the  form  of  differ- 
ences between  the  symbol  and  the  object  represented,  and  frequently 
also  in  the  spatial  detachment  of  the  symbol  from  the  object.  These 
diversities  are  often  the  sources  of  important  characteristic  advan- 
tages. In  certain  cases  a  name  or  symbol  confers  a  kind  of  substan- 
tial individuality  upon  an  otherwise  vague  and  uncertain  entity. 
Other  persons  before  the  time  of  Priestley  had  obtained  oxygen  but 
he  is  regarded  as  its  discoverer,  in  part  because  he  first  gave  it  a 
name. 

The  development  of  uniformities  and  diversities  in  connection 
with  symbols  also  leads  to  the  fruits  which  are  characteristic  of 
uniformities  and  diversities. 

Symbols  Mean  Various  Externalities 

Symbols  are  not  only  themselves  a  useful  auxiliary  but  they 
facilitate  the  application  of  other  externalities  in  connection  with  a 
given  domain  of  material.  Thus  by  their  conciseness  they  open  the 
way  for  the  formation  of  short  tabulations  or  other  brief  combina- 
tions of  various  materials,  and  for  the  use  of  reciprocal  externality 
among  these  materials  and  the  application  of  outside  externality  to 
them  in  group  ways.  An  important  special  case  of  this  source  of 
efficiency  is  the  use  of  maps  and  charts  of  various  kinds.  The 
use  of  symbols  frequently  leads  to  externality  in  the  form  of  sus- 
pended operations,  and  consequent  economies  such  as  are  involved  in 
cancellations  for  example. 

Also  the  process  of  contracting  material  into  symbols  often  leaves 
vacant  space  where  externalities  can  be  annexed,  or  indirect  routes 
or  methods  followed. 


SYMBOLISM  177 

By  taking  advantage  of  the  detachment  of  symbols,  the  mind  also 
acquires  a  certain  freedom  and  largeness  in  its  operations  which  are 
attended  by  many  useful  results. 

The  externalities  inextricably  inwoven  with  our  visual  habits  and 
those  due  to  the  permanency  and  easy  motion  of  symbols  may  also 
be  mentioned  in  this  connection. 

The  above  species  of  externality  often  occur  in  complex  form. 
Thus  in  solving  a  given  problem,  the  use  of  symbols  often  enables 
one  to  plunge  into  the  middle  of  the  subject,  and  to  work  in  several 
directions  at  once,  using  many  auxiliaries  simultaneously. 

Facilitate  Directive  Work 

The  smallness  and  lightness  of  symbols  facilitate  the  directive 
use  of  them  and  hence,  in  effect,  of  the  materials  which  they  repre- 
sent. The  useful  results  of  such  directive  use  are  discussed  in 
Chapter  XI  (p.  192).  Symbolism,  especially  in  the  form  of  the  effi- 
ciental  essence  of  an  object,  often  leads  to  important  directive 
efficiency  acts  of  other  kinds.  This  consists  in  regarding  an  object 
as  a  multiplicative  group  structure  in  which  the  efficiental  essence 
is  the  prime  group.  Often  the  essentials  of  a  desired  object  can 
be  found  in  some  accessible  or  cheap  form,  and  the  supplementary 
details  treated  in  some  special  way. 

Unexpected  and  Self-developing  Results 

The  use  of  symbols  often  also  leads  to  certain  unexpected  and  self- 
developing  results.  These  dialectic  results  often  spring  from  the 
unrealized  manifold  nature  of  symbols,  from  their  concentration, 
reciprocal  action,  and  the  various  uniformities  and  diversities  which 
characterize  them,  or  to  which  they  give  rise.  This  dialectic 
development  is  often  vague  and  uncertain,  in  other  cases  it  is 
standard  and  to  a  certain  degree  dependable  as  in  the  processes  of 
mathematics  or  other  calculuses. 

It  is  well  to  note  in  this  connection  that  the  dialectic  power  in  a 
calculus  in  large  measure  may  be  resolved  into  the  dialectic  proper- 
ties of  symbolisms  outlined  above.  Thus  the  approximate  uniform- 
ity in  the  size  of  the  symbols  employed  in  an  algebraic  equation  leads 
to  many  important  results  which  we  cannot  stop  to  point  out  in  detail. 
The  same  is  true  of  the  uniformity  in  the  size  of  the  letters  of  the 
alphabet,  and  of  Arabic  numerals.     For  these  ?.nd  like  reasons,  in 


178  SOURCES  OF  EFFICIENCY 

mathematical  work  a  symbolism  often  seems  to  move  forward  to 
new  results  by  some  intrinsic,  uncanny,  and  irresistible  power.  Hence 
the  mathematician  Euler,  for  example,  remarked  that  his  pencil 
seemed  at  times  to  surpass  himself  in  intelligence. 

Transcendent  Results 

Some  of  the  fruits  obtained  by  the  use  of  symbols  are  transcen- 
dental and  absolute,  in  the  sense  that  they  cannot  be  measured. 
An  instance  is  the  saving  of  lives  of  the  passengers  on  a  sinking 
ship  by  the  aid  of  wireless  telegraphy.  Others  are  unique  in  the 
sense  that  apparently  they  could  not  have  been  obtained  in  any  other 
way.  Thus  it  is  scarcely  conceivable  that  certain  highly  developed 
forms  of  multiplicative  groups  could  have  been  obtained  or  kept 
in  operation  without  the  aid  of  symbolisms. 

Another  illustration  of  a  like  high  order  of  fruitage  is  the  pleasure 
afforded  by  a  symphony  or  great  painting.  Still  another  of  widely 
different  character  is  the  power  conferred  on  us  by  symbols  to  use 
together  toolages  apparently  contradictory,  and  to  get  the  advantages 
belonging  to  each  with  a  further  dialectic  of  advantageous  results. 
An  illustration  is  the  use  in  combination  of  the  atomic  and  ether 
theories  of  matter. 

The  above  functions  of  symbols  may  be  complexed  in  many 
ways.  Illustrations  of  such  complex  useful  results  are  given  in  the 
paragraphs  which  follow. 

Increasing  Use  of  Symbols 

The  value  of  symbolisms  may  be  realized  in  other  more  pictorial 
ways,  as  by  noting  that  increasing  civilization  has  been  marked 
by  an  increasing  volume  and  variety  of  symbolisms.  This  value 
may  also  be  made  evident  by  trying  to  conceive  what  the  modern 
world  would  become  if  its  various  languages,  signs,  and  symbols 
were  removed.  Evidently  the  most  elementary  processes  of  life 
would  be  greatly  diminished  in  efficiency  while,  apparently,  the 
higher  and  complex  processes  would  crumble  and  disappear. 

Words  which  show  the  Value  of  Symbolisms 

The  value  of  symbolisms  may  be  realized  from  another  point  of 
view  by  recalling  and  massing  together  the  utilities  implied  by 
such  words  as  language,  plans,  scheme,  outline,  diagrams,  metaphors, 
paintings,  sculpture,  photography,  pictures,  art,  telegraph,  telephone. 


SYMBOLISM 


179 


Dangers  and  Limitations 

The  dangers  and  limitations  connected  with  the  use  of  symbols 
are  especially  prominent  on  account  of  the  abstract,  detached,  and 
often  highly  transformed  character  of  this  instrument  of  efficiency. 
The  following  diagram  will  be  an  aid    <,  j,, 

in  grouping  and  grasping  these  draw- 
backs. In  the  diagram  O  stands  for  the 
object  symbolized;  S  means  the  symbol 
for  O;  S'  is  the  symbol  after  it  has 
been  transformed  or  shifted  in  position 


for  some  purpose;  and  O'  is  the  object  ^ 
again  but  often  in  a  new  relation  or  condition.  This  diagram 
makes  clear  that  there  are  three  main  classes  of  dangers  connected 
with  the  use  of  symbols : 

(i)  Those  in  going  from  O  to  S  (that  is,  from  the  object  to  the 
symbol)  ; 

(2)  Those  in  going  from  S  to  S'  (that  is,  from  the  symbol  to  the 
symbol  in  a  new  position  or  state)  ; 

(3)  Those  in  going  from  S'  to  O'  (that  is,  from  the  symbol  back 
to  the  object). 

Errors  in  Going  from  Object  to  Symbol 

In  class  (i)  are  included  all  those  cases  where  the  symbol  fails 
to  correspond  to  the  object  which  it  is  supposed  to  represent.  A 
common  example  is  the  over-capitalization  of  a  stock  company.  The 
lack  of  correspondence  between  fact  and  symbol  may  be  due  either 
to  unconscious  error  or  to  intention.  In  the  latter  class  would  come 
various  misrepresentations,  lies,  and  swindles.  An  extreme  case  is 
that  where  a  symbol  is  wholly  deceptive  and  stands  for  nothing, 
or  what  is  worse  than  nothing,  as  in  some  cases  of  forgery. 

Errors  in  Manipulation  of  Symbols 

As  illustrations  of  class  (2)  we  have  the  errors  made  in 
transcribing  and  combining  symbols  in  mathematical  calculations,  or 
those  made  in  processes  of  reasoning  carried  on  in  oral  or  printed 
language.  Details  concerning  such  errors  are  given  in  Chapter 
XVI.  In  this  class  also  belong  losses  due  to  difficulties  in  preserv- 
ing symbols  till  the  time  is  ready  for  their  translation  back  into  the 
data  represented.     As  instances  we  have  the  cases  where  paper 


l8o  SOURCES  OF  EFFICIENCY 

money  and  various  memoranda  and  securities  have  been  destroyed 
by  fire,  flood,  insects,  or  rodents  before  the  valuable  symbols  named 
could  be  converted  into  some  concrete  and  permanent  form  of  wealth. 
Alterations  made  in  symbols  for  the  purposes  of  deception,  as  when  a 
check  is  raised,  also  belong  to  this  class  of  dangers  and  losses. 

Errors  in  Going  from  Sjnnbol  back  to  Object 

Class  (3)  includes  all  errors  and  misrepresentations  made  in  the 
process  of  converting  the  symbol  into  the  material  represented,  or 
some  datum  more  or  less  like  this  material.  An  important  case 
in  this  class  is  that  which  assumes  that  the  object  will  have  all  the 
properties  of  the  symbol,  as  that  a  bridge  will  be  as  strong  in  pro- 
portion to  its  size  as  in  the  model  which  has  been  made  to  repre- 
sent the  bridge.  Another  special  case  in  this  class  is  the  ignorant 
selling  of  stock  certificates  for  less  than  they  are  worth,  or  signing 
any  important  document  under  the  impression  that  one's  signature 
has  an  entirely  different  meaning  from  the  actual  one. 

An  extreme  case  in  this  class  is  the  error  of  regarding  the  symbol 
as  not  representative  but  ultimate.  Instances  are  the  common  error 
of  mistaking  paper  money  for  real  money,  or  of  exalting  a  religious 
image  or  ceremony  above  the  reality  represented.  This  conception 
of  the  symbol  as  an  objective  reality  rather  than  as  an  instrument 
for  attaining  results  often  takes  partial  and  elusive  forms.  Thus 
many  of  the  difficulties  in  the  mastery  of  mathematics  come  from 
regarding  such  symbols  as 

—  dy 

as  objects  rather  than  as  instruments. 

The  Tongue  of  Efficiency 

On  the  whole,  however,  it  is  evident  that  the  advantages  con- 
nected with  the  use  of  symbols  far  outweigh  the  disadvantages. 
In  fact  symbolism  may  be  termed  the  tongue  of  efficiency,  and  in 
some  respects  also  its  brain. 

SOURCES   OF   EFFICIENCY   IN   SYMBOLISM 

Our  study  of  symbolism  up  to  this  point  has  made  it  clear  that  a 
symbol  is  a  special  form  of  group,  and  that  the  utilities  which  flow 
from  the  use  of  symbols  are  special  forms  of  the  benefits  which 


SYMBOLISM  l8l 

accompany  the  employment  of  groups.  Hence  as  an  aid  to  using 
symbols  in  the  most  efficient  way  it  is  important  to  investigate  as 
closely  as  we  can  the  relation  of  symbols  and  symbolisms  to  the 
group  idea. 

The  Symbol  as  a  Group 

The  word  symbol  means  something  thrown  together;  that  is,  a 
contraction,  abbreviation,  or  syncopation.  Hence  primarily  symbol 
means  a  group  formed  by  the  process  of  inclusion.  Special  mention 
should  be  made  of  the  fact  that  this  contraction  is  made  in  such 
a  way  as  to  bring  in  front  of  the  user  and  within  the  scope  of  a 
single  act  of  vision,  data  that  may  have  been  lying  in  many  direc- 
tions and  at  various  distances  from  the  observer. 

The  process  of  contraction  by  which  symbols  are  formed  may  be 
carried  on  in  such  a  way  as  to  make  the  resulting  symbol  a  multi- 
plicative group  structure ;  or  later,  by  use  of  externality,  the  symbol 
may  be  developed  into  this  form.  Also,  as  has  been  pointed  out, 
different  symbols  are  frequently  combined  so  as  to  form  a  systemat- 
ically grouped  aggregate.  The  symbolic  multiplicative  group  system 
is  often  parallel  to  a  multiplicative  group  system  of  material  in  the 
object  represented. 

A  Symbol  as  a  Unit 

In  some  aspects  or  cases,  a  symbol  is  a  unit  which  has  various 
multipliers  or  multuses.  For  example  a  gesture  which  causes  an 
entire  audience  to  rise  to  its  feet  is  a  unit  motion  with  respect  to 
the  motion  of  the  audience  which  follows.  So  a  word  in  some  re- 
spects is  a  unit  with  respect  to  the  object  represented  by  the  word. 
A  symbol  may  also  be  a  multiplier.  Thus  a  gold  reserve  is  in  effect 
multiplied  many  times  by  the  large  amount  of  paper  money  circu- 
lated with  reference  to  it. 

Relation  of  Symbolism  to  other  Efficients 

With  respect  to  the  principle  of  orders  of  material,  symbols  are 
usually  high  in  the  scale  of  efficiency,  and  often  indeed  belong  to 
the  efficiental  abstract  grade. 

Externalities  of  various  kinds  are  present  or  implied  in  symbols. 
Beside  the  various  species  of  related  externality  spoken  of  in  the 
preceding  pages  mention  may  be  made  of  the  fact  that  a  symbol 


l82  SOURCES  OF  EFFICIENCY 

implies  a  wide  range  of  application,  and  also  certain  auxiliaries  to 
safeguard  the  use  of  the  symbol. 

In  addition  to  the  various  uniformities  and  diversities  which 
have  already  been  considered  as  prominent  in  symbolisms,  special 
mention  should  be  made  of  the  exact  correspondence,  or  uniformity, 
which  should  exist  between  symbol  and  object,  and  between  symbols 
representing  the  same  object. 

Some  element  of  limitation  is  always  a  contributing  cause  to  the 
formation  and  use  of  symbols.  Thus  if  it  were  not  for  our  limited 
grasp  of  objects  in  space  and  time,  we  should  not  need  to  use  sym- 
bols. This  limitation  factor  varies  greatly  in  degree  and  form. 
Hence  a  special  study  of  it  will  be  an  important  aid  to  the  most 
efficient  use  of  symbols  in  different  cases.  For  this  special  study 
see  Chapter  XV  (p.  265). 

Relativity  of  Sjmibols 

This  brings  us  to  the  general  matter  of  relativity  in  the  nature 
symbols.  With  reference  to  different  individuals  and  to  the 
same  individual  under  different  circumstances  there  is  often  much 
variation  as  to  what  is  to  be  taken  as  a  primal  datum  of  experience 
and  what  is  to  be  regarded  as  an  artificially  formal  symbolism. 
Thus  the  colored  surface  of  an  object  from  one  view  point  is  an 
original  datum  of  experience  which  may  usefully  be  denoted  by 
symbols  (described  in  words,  or  expressed  in  units  of  area)  ; 
from  another  standpoint  this  colored  surface  is  but  a  symbolic  repre- 
sentation of  the  certain  molecules  and  forces. 

A  symbol  also  contains  an  element  of  unique  individuality,  not 
statable  in  terms  of  other  concepts  or  primal  modes  of  efficiency. 
This  often  becomes  the  source  of  unexpected  uses  and  values. 

Definition 

As  a  summary  of  the  results  of  our  study  of  the  nature  of 
symbols  we  may  make  the  following  definition: 

A  symbol  (or  symbolism)  is  a  group  (or  system  of  groups)  whose 
function  is  the  efficient  expression  and  transfer  of  other  groups  and 
which  acts  mainly  through  the  eye  and  ear. 

METHODS  OF  APPLICATION 

A  realization  of  the  essentially  multiplicative  nature  of  symbolism 
is  an  aid  in  many  ways  in  making  the  most  effective  use  of  signs  and 


SYMBOLISM  183 

representatives.  Many  of  these  methods  are  obvious  and  we  shall 
discuss  only  those  which  are  most  important  or  most  likely  to  be 
overlooked. 

Vast  Number  of  Possible  Symbolisms 

By  an  application  similar  to  that  made  with  the  other  Efficients, 
the  multiplicative  principle  aids  us  in  realizing  the  great  number  of 
possible  materials  and  combinations  of  material  which  can  be  utilized 
in  making  symbols.  It  also  aids  us  in  conceiving  the  vast  number 
of  forms  which  symbolisms  may  assume.  The  multiplicative  group 
principle  is  likewise  a  powerful  help  in  systematizing  these  materials 
and  forms  and  holding  them  ready  for  use. 

Potency  of  Symbolisms 

The  great  power  in  the  multiplicative  principle  enables  us  to  realize 
also  the  extreme  extent  and  efficiency  to  which  even  a  limited  or 
crude  species  of  symbolism  may  be  developed.  Illustrations  are 
the  power  of  the  tactual  symbolisms  employed  by  a  person  like  Helen 
Keller,  and  those  special  forms  unconsciously  employed  by  un- 
tutored lightning  calculators.  As  a  more  abstract  illustration  we 
have  the  power  of  the  equation  ax^  +  bxy  +  cy-  -\-  dx  -\-  ey  -{- 
f  =z  0  to  represent  all  the  properties  of  the  straight  line,  circle, 
ellipse,  parabola,  and  hyperbola. 

Adapting   Symbolisms  to  Special  Circumstances 

Owing  to  the  great  variety  of  forms  which  symbols  and  symbolisms 
may  take,  and  the  wide  differences  in  the  circumstances  attending 
their  use,  in  any  specified  case  it  is  of  especial  importance  to  study 
the  limitations  and  possibilities  involved  in  order  to  select  or  devise 
the  most  desirable  symbolism  for  use  in  the  given  situation.  In  this 
process  much  use  of  externality  is  often  desirable.  Thus  in  making 
a  graph,  or  realizing  an  efficiental  essence,  especially  in  a  difficult 
case,  externality  is  frequently  helpful.  This  may  take  the  form  of 
getting  at  a  distance  from  (or  holding  at  arm's  length)  the  material 
considered,  or  of  viewing  it  from  all  sides,  or  of  allowing  time 
to  work  upon  it.  Also  when  a  wide  domain  is  studied,  the  efficiental 
essence  is  apt  to  come  to  the  surface  in  certain  spots,  or  a  natural 
symbolism  to  be  revealed. 

Cases  illustrative  of  the  advantage  and  need  of  special  symbolisms 


l84  SOURCES  OF  EFFICIENCY 

under  different  circumstances  are  the  use  of  adapted  marks  and 
signs  on  clay  tablets  in  Babylonia  and  Assyria,  on  papyrus  and 
granite  in  Egypt,  and  parchment  and  marble  in  Greece.  A  modern 
instance  is  the  difference  between  day  and  night  signals  on  railroads. 
An  illustration  from  the  world  of  commerce  is  the  fact  that  cotton 
and  wheat  may  be  sold  by  standard  (that  is,  technical  verbal  descrip- 
tion as  Grade  A,  etc.),  while  wool  cannot  be  sold  in  this  convenient 
way  but  is  bargained  for  by  sample. 

Relations  of  Graphic  and  Linguistic  Symbolisms 

As  to  the  use  of  more  general  kinds  of  symbolisms  under  different 
circumstances,  it  should  be  observed  that  algebraic  symbolism 
(Class  II,  p.  173)  is  preferable  as  a  general  or  standard  method 
of  expression,  while  graphic  or  pictorial  symbols  are  to  be  used 
locally  or  occasionally  for  the  sake  of  special  advantages.  Examples 
of  such  local  use  are  the  employment  of  flags  in  the  management 
of  an  army,  or  of  diagrams  in  the  teaching  of  grammar. 

Careful  study  must  often  be  made  as  to  when  and  how  to 
combine  these  two  main  classes  of  symbols.  A  rhythmic  or  alternate 
use  of  the  two  will  often  be  found  very  advantageous. 

Form  and  Color  in  Symbolisms 

Also  in  devising  and  using  symbols  it  is  to  be  noted  that,  in 
general,  the  form  of  a  symbol  is  a  more  effective  element  than  the 
color.  This  is  one  reason  why  algebraic  symbolism,  as  a  rule,  is 
superior  to  the  graphic  form.  For  a  somewhat  similar  reason  spoken 
language  is  more  efficient  than  gesture  language  as  a  standard  method 
of  expression.  Vocal  language  also,  since  it  employs  certain  organs 
in  the  mouth  and  throat,  has  the  advantage  of  leaving  the  arms  and 
hands  free  for  use  in  other  ways. 

Standard  and  Special  Symbolisms 

In  the  field  of  objective  symbolisms  (that  is,  of  those  used  not  for 
private  purposes,  but  in  connection  with  other  people)  it  is  desirable 
to  give  the  preference  to  standard  and  conventional  symbols.  At 
the  same  time  it  is  important  to  acquire  the  power  and  form  the 
habit  of  improvising  symbols  for  one's  private  use,  since  such 
symbols  may  often  be  highly  efficient  in  special  situations. 


SYMBOLISM  185 

Preference  to  Symbols  of  High  Order 

It  is  scarcely  necessary  to  say  that  it  is  desirable  to  make  all 
symbols  and  symbolisms  of  as  high  an  order  as  circumstances  will 
permit.  In  the  first  place  the  material  to  be  symbolized  should  be 
selected  and  transformed  so  as  to  make  it  as  efficient  as  possible. 
Again  individual  symbols  should  be  as  efficient  as  possible  both  in 
form  and  in  other  ways.  As  examples  of  superior  symboHsms  in 
this  respect  we  have  the  phonetic  alphabet  as  compared  with  the 

Egyptian  hieroglyphs,  the  Leibnitzian   -^   as  contrasted  with  the 

Newtonian  y,  and  the  use  of  a  word  like  Jehovah  in  expressing 
infinite  external  multiplicative  power  as  compared  with  a  heathen 
idol. 

Also  in  a  symbolism  of  high  order  the  individual  symbols  are 
combined  in  effective  ways,  as  for  example  in  a  multiplicative  group 
system.  By  this  method,  for  instance,  a  few  symbols  rightly  used 
are  made  to  take  the  place  of  a  large  number  combined  in  an 
inefficient  way.  An  example  is  the  English  alphabet  as  compared 
with  the  Chinese  syllabic  system.  A  more  specific  instance  is  the 
Linnean  method  of  naming  species  of  plants  and  animals.  Before 
the  time  of  Linneus  one  name  of  common  blue  grass  was  "gramen 
pratense  paniculatum  majus  latiore  folio  poa  theophiasti".  In 
the  Linnean  system  of  nomenclature  this  name  is  reduced  to  "'poa 
pratensis".  The  swift  and  vast  progress  of  botany  and  zoology 
since  the  time  of  Linneus  is  largely  due  to  the  simplicity  and  power 
which  characterize  the  binomial  method  of  naming  species. 

A  high  order  of  syrnbolism  often  takes  the  form  of  a  symbolism 
of  a  symbolism,  as  when  shorthand  is  used  instead  of  ordinary 
language.  Again  it  may  take  the  dimensional  form,  as  when  a 
solid  is  represented  by  a  flat  picture,  or  in  some  cases  by  a  set  of 
points,  or  even  by  one  point. 

In  this  connection  it  is  to  be  remembered  that  neighborhood  sym- 
bolisms (see  p.  167)  are  of  a  high  order  of  efficiency,  and  that  they 
can  often  be  utilized  not  only  in  private  provisional  symbolisms,  but 
also  in  giving  added  economy  and  power  to  certain  applications 
of  objective  language. 

Similarly  a  manifold  symbolism  is  of  a  high  order  of  efficiency. 
An  example  is  that  of  expressing  the  fact  that  a  given  bottle  con- 
tains poison  by  printing  the  word  poison  on  the  label,  annexing  a 


l86  SOURCES  OF  EFFICIENCY 

picture  of  a  skull  and  crossbones,  and  making  the  surface  of  the 
bottle  rough  to  the  touch. 

Auxiliaries  in  Making  and  Using  Symbolisms 

In  applications  of  symbolism,  other  forms  of  externality  than 
those  already  indicated  are  often  extremely  useful.  For  instance 
the  use  of  some  auxiliary  often  makes  it  possible  to  obtain  pictures 
or  other  representations  of  an  object  not  otherwise  possible.  A 
striking  instance  of  this  are  the  skiagraphs  of  the  bloodvessels  of 
the  brain  obtained  by  the  injection  of  mercury  into  these  blood- 
vessels, and  the  application  of  X  rays.  In  other  cases  extra  and, 
from  the  strictly  logical  point  of  view,  superfluous  symbolism  fre- 
quently results  in  quickness  and  vigor  of  action  with  a  consequent 
dialectic  of  values.  Instances  of  this  are  the  method  of  denoting  the 
end  of  a  sentence  by  a  period  or  dot  and  also  by  the  use  of  a  capital 
letter  at  the  beginning  of  the  next  sentence;  or  the  employment  of 
difference  of  shape  as  well  as  size  in  forming  a  symbol  as  when 
A  is  used  instead  of  /3^  as  the  capital  form  of  small  a.  A  combination 
of  color  and  form  in  a  symbol  when  either  alone  would  be  adequate 
is  a  like  instance. 

A  more  general  and  important  case  is  supplied  by  the  manifold 
and  various,  even  profuse,  symbolism  in  a  language  like  English  as 
compared  with  a  minimal  language  like  Esperanto  or  Volapuk.  Here, 
as  has  been  said,  "luxury  is  economy",  and,  we  may  add,  efficiency. 

This  apparent  excess  of  symbolism  is  useful  not  only  as  a  direct 
source  of  efficiency  but  often  also  in  a  negative  way  as  a  means  of 
preventing  error.  For  example  it  often  furnishes  simple  means  of 
checking  a  given  statement  or  process. 

Utilization  of  the  Self-developing  Power  in  Symbolisms 

Especially  important  also  is  it  to  recognize  and  utilize  the  self- 
corrective  and  self -developing  property  which  is  peculiarly  charac- 
teristic of  symbolism  as  a  source  of  efficiency.  This  principle  will 
be  found  particularly  useful  in  cases  of  limitation  and  difficulty,  as 
when  we  express  in  language  all  that  we  know  about  partially  under- 
stood matters  and  find  by  development  of  this  symbolism  that  our 
language  proves  to  possess  a  far  wider  expressiveness  than  we  had 
supposed.  In  its  higher  forms  this  principle  is  illustrated  by  the 
extraordinary  power  of  certain  symbolic  forms  of  deductive 
reasoning. 


SYMBOLISM  187 

Ideal  Species 

It  follows  from  what  has  been  said  in  the  preceding  pages  that 
our  ideal  form  of  symbolism  would  be  a  representation  of  efficiental 
data  in  efficiental  form  for  efficiental  ends. 

Summary  of  Chapter 

An  illustration  of  the  great  efficiency  value  of  symbols  is  the  fact 
that  making  a  written  record  of  a  result  opens  the  way  to  the  reuse 
of  the  given  result  in  many  lines.  Among  the  most  obvious  kinds  of 
symbolisms  are  written  and  oral  language,  pictures,  maps,  tabula- 
tions, motions,  and  combinations  of  these.  More  extreme  species 
are  neighborhood  symbolism,  and  the  expressive  use  of  absence  or 
emptiness.  Symbols  are  thus  not  only  composed  of  a  great  di- 
versity of  materials,  but  they  also  occur  in  an  endless  variety  of 
forms.  Among  the  most  important  forms  of  symbolisms  are  the 
different  linear  and  areal  species,  and  those  which  are  built  upon 
each  other  in  succession.  The  two  most  general  types  are  the 
geometric  and  algebraic  (or  the  direct  and  indirect).  Its  efficiental 
essence  is  often  a  highly  important  representative  of  an  object  or  a 
domain  of  material. 

The  economy  attained  by  using  the  symbol  of  an  object  instead 
of  the  object  itself  is  often  practically  infinite.  Other  values  which 
frequently  result  are  speed,  organization,  ease  in  directive  manage- 
ment and  in  the  application  of  externality,  the  fruits  of  these,  and 
other  useful  results  which  are  often  transcendent.  Each  particular 
form  of  symbolism  has  its  own  special  efficiency  powers.  However, 
owing  to  the  detached  and  abstract  nature  of  most  symbols  their  use 
is  exposed  to  peculiar  dangers  which  must  be  guarded  against. 

Owing  to  the  great  variety  of  existing  or  possible  symbolisms  and 
their  extreme  power,  great  care  is  often  needed  in  order  to  select  or 
invent  the  particular  species  which,  in  a  given  case,  will  be  most 
effective.  Especial  attention  is  to  be  paid  to  the  use  of  different 
kinds  of  symbolism  in  combination,  as  in  the  alternate  use  of  the 
two  principal  kinds.  The  application  of  externality  is  useful  in 
different  cases.  Preference  is  to  be  given  to  standard  forms  of  high 
order,  the  highest  form  of  all  being  that  which  is  as  efficiental  as 
possible  both  as  to  data,  form,  and  aim. 


l88  SOURCES  OF  EFFICIENCY 

EXERCISE  10 
State  the  class  or  classes  to  which  each  of  the  following  symbols  or  sym- 
bolisms  belongs : 

1.  A  smile  3.  Footprints  5.  A  trade  mark 

2.  A  flag  4.  Ditto  marks  6.  A  weather  vane 

7.  Sounds  made  by  sleigh  bells. 

8.  The  word  rock  in  "He  was  a  rock  in  defence  of  bis  position". 

9.  A  curved  line  showing  the  fluctuations  of  the  price  of  wheat  from  day 
to  day. 

10.  The  sign  +  as  used  to  express  addition. 

11.  A  coat  of  arms  as  used  in  heraldry. 

12.  The  cry  of  an  infant  when  in  pain. 

Give  an  example  of  the  use  of  each  of  the  following  as  a  symbol : 

13.  Some  bird  17.  Heat  21.  Some  other  fluid 

14.  Some  quadruped  18.  Flame  22.  The  air 

15.  Some  flower  19.  Some  metal  23.  Smoke 

16.  Some  tree  20.  Water  24.  A  leaf 

25.  A  physical  force  to  represent  a  mental  power 

26.  State  the  advantages  involved  in  the  use  of  each  symbol  given  in  Exs. 
1-12. 

27.  Name  all  the  audible  symbols  you  can. 

28.  All  the  visible  ones. 

29.  All  the  mental  ones, 

30.  Give  an  example  of  order  used  as  a  symbol. 

Give  an  example  of  the  following  classes  of  symbols  or  symbolisms : 

31.  Natural  35.  Neighborhood  39.  Multiplicatively  grouped 

32.  Artificial  36.  Inherited  40.  Semi-linear 

33.  Semi-artificial        37.  Dual  41.  Of  second  order 

34.  Negative  38.  Triple  42.  Of   third   otder 

43.  What  different  kinds  of  symbolism  are  combined  in  a  rocket  fired  as 
a  signal? 

44.  In  a  flash  light  as  used  by  a  light  house? 

45.  Name  some  of  the  most  important  signs  of  spring,  and  state  the  class 
or  classes  of  symbols  to  which  each  of  these  belongs. 

46.  If  it  costs  $3000  per  year  to  maintain  a  given  light  house  and  $150,000 
worth  of  property  is  saved  by  means  of  the  light  house,  state  the  degree  of 
efficiency  involved. 

47.  During  one  year  the  expenses  of  a  certain  business  were  $10,000  and 
the  returns  were  $16,000.  The  next  year  $1000  additional  spent  in  advertising 
increased  the  profits  of  the  business  by  $4000.  State  the  degree  of  efficiency 
of  the  business  the  second  year  as  compared  with  the  first.  State  the  de- 
gree of  efficiency  of  the  additional  money  spent  in  advertising. 

48.  State  the  advantages  in  the  use  of  a  set  of  signals  in  playing  football. 
Also  the  disadvantages. 

49.  Discuss  the  principles  of  symbolism  involved  in  moving  pictures.  Also 
the  efficiental  and  other  advantages  which  result. 


SYMBOLISM 


189 


50.  Answer  the  question  "What's  in  a  name". 

Give  an  instance  where  the  use  of  symbols  leads  to 

51.  An  economy  of  material  54.  Reuse 

52.  An  economy  of  force  55.  Multuse 

53.  An  economy  of  time  56.  Formation  of  a  group 

57.  Formation  of  a  multiplicative  group  system 

58.  Formation  of  an  order  of  materials  series 

59.  Self-developing  efficiency  results 

State  approximately  the  degree  of  efficiency  involved  in  the  use  of 

60.  "Five"  as  a  substitute  for  "four  and  one  more". 

61.  6792  for  "six  thousand  seven  hundred  and  ninety-two". 

62.  4  -{-  2  =:  6  for  "four  and  two  are  six". 

63.  In  1,987,653  the  figure  3  expresses  three  units  and  it  also  helps  the 
figure  5  to  express  tens,  6  to  express  thousands,  etc.  How  many  items  of 
work  does  it  do  in  all?  How  many  kinds  of  symbolism  are  combined  in  this 
instance  ? 

64.  Give  an  example  of  symbolism  of  the  third  order  with  a  statement  of 
the  efficiencies  connected  with  it. 

65.  Give  two  examples  of  the  use  of  protective  coloration  in  animals,  and 
explain  its  benefits. 

66.  What  is  the  smallest  number  of  points  needed  in  order  to  represent 
a  straight  line?  A  plane  surface?  What  is  the  degree  of  efficiency  in  each 
of  these  cases? 

Name  as  many  advantages  as  you  can  connected  with  the  use  of 

67.  Maps  68.  The   electric  telegraph  69.  Wireless   telegraphy 

70.  What  is  the  semaphore  and  what  principles  of  symbolism  are  em- 
bodied in  it? 

71.  State  the  different  forms  of  symbolism  which  are  often  used  in 
making  an  exhibit  of  the  expenditures  of  a  city,  and  the  results  obtained. 
What  are  the  advantages  of  such  symbolic  summations? 

72.  Discuss  the  advantages  in  the  use  of  a  trade  mark. 

73.  Give  two  examples  of  graphic  (or  geometric)  symbolism.  Also  two 
of  algebraic  symboHsm. 

74.  Give  an  example  where  graphic  and  algebraic  symbolism  are  used  to 
advantage  in  alternate  succession. 

75.  State  as  many  different  kinds  of  symbols  as  you  can  which  can  be  used 
in  advertising  a  business,  and  illustrate  each. 

76.  By  numbering  the  parts  of  a  ship  and  keeping  a  model  of  the  ship 
at  some  shipyard,  it  is  often  possible  quickly  to  repair  the  ship  while  at  a 
distant  place.  Explain  how  this  may  be  done  and  what  principles  of  sym- 
bolism are  utilized  in  the  process.  Name  some  other  objects  besides  ships 
to  which  the  method  is  applicable. 

yy.  State  what  is  meant  by  routing  a  piece  of  work  in  a  factory,  the  ad- 
vantages involved,  and  how  routing  is  aided  by  symbolism. 

78.  What  kinds  of  symbolism  are  involved  in  social  etiquette?  What  ad- 
vantages result?    What  disadvantages? 


I90  SOURCES  OF  EFFICIENCY 

79.  Give  an  example  of  a  symbol  which  has  erroneously  come  to  be  used 
as  a  reality. 

80.  Discuss  the  disadvantages  in  the  use  of  symbolisms  implied  in  the 
statement,  "talk  is  cheap". 

81.  Give  two  illustrations  of  errors  or  losses  arising  from  the  use  of 
symbolisms. 

82.  State  as  many  checks  as  you  can  on  the  abuse  of  symbols. 

83.  Express  as  well  as  you  can  the  unused  wealth  of  symbolic  power  in 
the  alphabet. 

84.  Explain  the  Dewey  method  of  classifying  books  and  the  principles  of 
symbolism  utilized  in  it.  Indicate  other  fields  in  which  this  method  of 
classifying  objects  is  used  or  is  usable. 

85.  In  what  respects  do  actions  speak  louder  than  words? 

86.  It  was  the  habit  of  Clerk  Maxwell  from  early  childhood  to  try  to 
discover  what  he  called  the  "go",  or  the  "particular  go",  of  any  machine  or  in- 
strument which  he  saw.  In  terms  of  the  ideas  of  the  present  chapter  explain 
the  meaning  of  the  word  "go"  as  thus  used. 

87.  Discuss  the  relation  of  symbolism  to  efficiental  essence.  For  instance,  • 
which  of  the  two  terms  is  broader? 

88.  Why  should  the  letters  in  a  written  word  be  connected  or  run  to- 
gether, while  those  in  a  printed  word  are  distinct? 

89.  Explain  the  principles  of  symbolism  embodied  in  some  system  of  print 
for  the  blind. 

90.  Give  an  example  of  some  kind  of  equivalence  used  as  a  symbol  for 
surplusage  or  profit. 

91.  Give  an  instance  where  the  removal  of  an  object  or  domain  of  ma- 
terial to  a  distance  aids  in  revealing  its  efficiental  essence. 

92.  Give  an  instance  where  the  form  of  a  symbol  is  more  efficient  than 
its  color.     Also  give  one  where  the  reverse  is  true. 

93.  Discuss  the  relative  values  of  audible  and  visible  symbols. 


EXERCISE  11 
Review 

1.  Of  4000  eggs  which  were  placed  in  a  given  incubator,  2400  hatched. 
State  the  degree  of  efficiency  involved. 

2.  A  girl  can  write  15  words  per  minute  by  hand  and  60  words  by  type- 
writer. Express  in  two  ways  the  degree  of  efficiency  involved.  State  some 
of  the  sources  of  this  efficiency. 

3.  Make  up  and  solve  a  problem  of  your  own  concerning  the  degree  of 
efficiency  in  a  given  case  and  the  sources  of  this  efficiency. 

4.  Instead  of  paying  for  each  article  as  purchased,  it  is  often  an  advan- 
tage to  run  an  account  at  a  store,  and  to  pay  for  purchases  occasionally  by 
check.     State  the  Efficients  involved  in  the  latter  method. 

5.  What  principle  of  efficiency  is  utilized  in  the  wedge  form  of  attack  in 
warfare? 


SYMBOLISM  191 

6.  Why  is  it  often  an  advantage  for  a  baseball  player  to  train  himself  for 
batting  by  swinging  Indian  clubs  many  times  heavier  than  the  bat  which  he 
is  to  use?    What  principle  of  efficiency  is  involved? 

7.  Explain  the  addition  of  numbers  in  arithmetic  as  a  combining  of  multi- 
plicative groups.     What   advantages   result? 

8.  Treat  in  like  manner  the  multiplication  of  numbers. 

9.  Explain  division  of  numbers  with  reference  to  the  principles  of  groups. 
ID.  In  a  certain  county  clerk's  office  under  the  elective  system  in  a  given 

year  the  receipts  were  $13,968  and  the  expenditures  $23,928.  Later  under  the 
appointive  system  the  receipts  were  $31,355  and  the  expenditures  $20,200. 
Compute  the  degree  of  efficiency  involved.  State  some  of  the  possible 
sources  of  the  increased  efficiency. 

11.  What  principle  of  efficiency  is  most  prominent  in  the  following  pre- 
cept:    Be  sure  you  are  right  and  then  go  ahead? 

12.  What  principles  of  efficiency  are  involved  in  the  case  of  a  straw  which 
shows  which  way  the  wind  blows? 

13.  What  principle  of  efficiency  is  involved  in  the  use  of  a  baggage  check 
for  a  trunk,  and  what  advantages   result? 

14.  In  language  study  what  efficiencies  are  involved  in  using  the  principal 
parts  of  a  verb  as  representative  of  all  the  forms  of  the  verb? 

15.  A  boy,  sick  of  the  hook  worm  disease  was  found  to  be  12  per  cent 
efficient.  If  a  normal  boy  could  work  8  hours  a  day,  how  long  could  the 
sick  boy  work? 

16.  In  the  business  world  what  are  the  signs  of  the  beginning  of  a  period 
of  commercial  prosperity?  State  some  of  the  advantages  of  being  able  to 
read  these  signs. 

17.  Discuss  the  efficiency  values  of  artistic  surroundings  in  a  store  or  fac- 
tory, especially  of  those  symbolisms  which  convey  an  appreciation  of  the 
Efficients  in  some  way. 

18.  What  principles  of  efficiency  are  involved  in  Emerson's  statement  "The 
key  to  every  man  is  his  thought".  Give  illustration  of  the  uses  which  may 
be  made  of  this  statement. 

19.  As  a  result  of  the  use  of  Dalton's  chemical  units,  exact  methods  of 
making  sulphuric  acid  have  been  substituted  for  guess  work  and  rule  of 
thumb.    State  the  Efficients  involved  and  the  useful  results  obtained. 

20.  Discuss  the  relation  of  the  classification  of  objects  to  the  principles 
of  multiplicative  grouping. 


CHAPTER  XI 
DIRECTIVE 
Illustrations 

It  has  been  estimated  that  by  stocking  the  rivers  of  France  with 
black  bass  brought  from  America  the  value  of  the  fish  taken  annually 
from  the  French  streams  has  been  doubled.  The  transfer  of  the 
eucalyptus  tree  from  Australia  to  other  lands  as  California  and 
South  Africa  has  produced  even  more  important  results.  These  in- 
stances illustrate  the  efficiency  value  of  man's  power  to  change  the 
position  of  objects  including  himself.  Often  this  principle  takes 
various  complex  and  apparently  qualitatively  different  forms,  such 
as  the  changing  of  the  forms  of  objects,  the  selection  and  cultiva- 
tion of  plants,  and  the  cooking  and  preservation  of  their  products. 
But  the  primary  and  fundamental  principle  involved  in  all  such 
cases  is  that  of  changing  the  position  of  objects  or  parts  of  objects. 
This  principle  of  directive  action  constitutes  the  next  fundamental 
source  of  efficiency  which  we  shall  study.  We  shall  denote  it  by  the 
single  word  directive. 

The  ways  and  forms  in  which  this  category  of  efficiency  comes  in- 
to play  are  so  numerous  and  so  often  complexed  with  other  Effi- 
cients that  we  shall  call  particular  attention  only  to  those  cases  where 
the  directive  principle  is  prominent  as  compared  with  the  other 
prime  sources  of  efficiency  which  are  involved. 

CLASSIFICATION 

Objects  which  may  be  directed 

Cases  of  directive  action  may  be  classified  according  to  the  mater- 
ials moved  or  directed  in  them.  In  general  we  may  say  that  any- 
thing may  be  moved,  changed,  or  directed  in  some  respects,  but  no 
object  can  be  moved  in  all  respects.  For  example  we  cannot  change 
the  position  of  the  moon  in  its  orbit,  but  by  shifting  our  position 
on  the  earth  we  can  change  the  position  of  the  moon  in  the  sky  with 
reference  to  other  heavenly  bodies.  We  cannot  change  the  amount 
of  rain  which  falls  from  a  cloud  but  by  irrigation  or  the  processes 

192 


DIRECTIVE 


193 


of  dry  farming  we  can  in  part  change  the  route  by  which  water 
travels  from  the  cloud  to  the  ocean  with  very  beneficial  results  to 
mankind.  We  cannot  live  over  the  past  directly,  or  make  two  plus 
two  equal  five,  but  we  can  do  both  of  these  things  in  some  indirect 
sense. 

As  a  result  of  what  has  been  said  it  is  evident  that  a  special 
science  of  directive  action  may  exist  in  each  of  the  principal  fields 
into  which  human  affairs  are  usually  divided.  Thus  we  have  civil 
engineering,  mechanical  engineering,  electrical,  social,  educational^ 
and  similar  departmental  species  of  management. 

Other  methods  of  classifying  directive  acts  are,  however,  more 
important  than  this  for  our  purpose. 

Directive  Agents 

One  of  these  is  a  grouping  of  directive  cases  according  to  the 
directive  agents,  that  is,  the  directors  involved.  All  the  various 
forms  of  what  is  called  a  living  matter  have  some  directive  power 
both  over  themselves  and  over  some  objects  external  to  themselves. 

Thus  various  plants  are  able  to  turn  themselves  (as  a  whole  or  in 
part)  toward  the  sun  (heliotropism),  or  toward  moisture  (hydro- 
tropism), or  toward  the  earth  (geotropism),  and  in  other  ways. 
Highly  specialized  forms  of  such  powers  are  illustrated  by  the 
sensitive  plants  and  the  Venus  flytrap.  Plants  also  have  power  to 
draw  food  from  the  earth  and  air,  and  also  to  move  such  food  for 
considerable  distances  in  opposition  to  the  force  of  gravitation.  Im- 
portant special  cases  are  the  power  which  protoplasm  has  to  direct 
sunlight  and  which  certain  plants  have  to  fixate  nitrogen. 

Individual  animals  have  many  different  ways  of  moving  themselves 
and  external  objects.  A  primitive  case  is  that  of  the  sea  urchin 
covering  itself  with  sea  weed  to  protect  itself  from  its  enemies. 

An  aggregate  of  individuals  may  also  constitute  an  important 
directive  agency.  Examples  are  a  flock  of  birds,  a  pack  of  wolves, 
a  society,  nation,  or  corporation. 

Similarly  it  is  often  useful  to  regard  certain  parts  of  individuals  as 
independent  directors.  Examples  are  the  cells  and  organs  in  a  living 
body,  and  the  different  so-called  faculties  of  the  mind. 

More  abstract  entities  also  have  what  constitutes  for  our  purpose 
directive  power;  illustrations  of  these  are  the  spirit  of  the  age,  the 
weltgeist,  or  any  aggregate  of  efficiency  agencies. 


194  SOURCES  OF  EFFICIENCY 

Also  in  efficiency  processes  allowance  must  be  made  for  unknown, 
or  imperfectly  known,  or  even  transcendental  efficiency  agencies. 

It  is  important  to  note  in  this  connection  the  wide  range  in  direc- 
tive powers  both  in  the  individual  agent,  and  in  different  directors 
when  compared  with  each  other.  The  oyster  when  young  has  con- 
siderable self-directive  power,  but  when  mature  has  very  little. 
With  man  the  reverse  is  true. 

In  self-directive  the  material  moved  and  the  agent  are  one. 

Directive  Acts  Classified  according  to  Form 

Most  important  of  all  for  our  purpose  is  the  classification  of 
directive  acts  according  to  their  form. 

A  simple  case  of  spatial  directive  is  that  of  changing  the  position 
of  an  object.  Changes  in  the  position  of  the  parts  of  an  object  may 
result  in  a  change  of  shape.  With  regard  to  the  category  of  space 
(or  quantity)  a  directive  act  may  also  be  narrow  or  comprehensive. 
More  important  still  it  may  be  a  separating  or  a  collecting  act ;  that 
is,  it  may  be  an  act  of  analysis  or  one  of  synthesis.  It  may  be  partial 
in  that  it  is  directive  of  some  part  of  an  object,  or  in  that  it  is  a 
transfer  of  an  object  in  some  specifically  limited  way.  It  may  be 
indefinite  as  when  a  situation  is  merely  agitated  or  stirred  up,  the 
motive  being  a  vague  hope  that  something  useful  may  result;  or 
definite,  as  when  every  step  and  the  reason  for  it  are  carefully 
calculated. 

An  act  of  directive  may  be  characterized  according  to  the  cate- 
gory of  number  in  various  ways  as  by  the  number  of  objects  moved, 
the  number  of  directors,  or  the  number  of  parts  in  the  given  act. 

A  simple  case  of  a  temporal  directive  act  is  the  transfer  of  an 
object  from  one  point  in  time  to  another.  An  example  is  the  saving 
of  money  to  be  used  at  some  future  date.  A  much  broader  case  is 
the  conservation  of  national  resources.  With  respect  to  time  a  direc- 
tive act  may  also  be  brief  and  temporary,  or  of  long  duration.  The 
adjectives  prophetic,  preventive,  or  well  timed  are  also  often  applic- 
able. An  important  temporal  species  is  that  termed  initiative,  that 
is,  the  act  or  power  of  making  a  start  (or  doing  all  that  the  be- 
ginning of  an  act  implies)  under  any  given  circumstances,  especially 
those  which  are  difficult. 

As  to  motion  and  force,  directive  acts  may  be  characterized  as 
feeble,  delicate,  energetic,  automatic,  slow,  or  swift. 


DIRECTIVE 


195 


An  important  species  is  what  may  be  termed  reciprocal  directive. 
In  the  simplest  form  of  this  case  each  of  two  agents  moves,  directs, 
or  influences  the  other  or  something  belonging  to  the  other,  A  large 
part  of  trade,  exchange,  and  commerce  belongs  to  this  form  of 
directive  action. 

With  respect  to  the  categories  of  mind,  various  cases  of  directive 
may  be  characterized  as  conscious,  unconscious,  and  subconscious; 
or  even  voluntary  and  involuntary.  Thus  certain  kinds  of  personal 
influence  are  unconscious  and  often  involuntary. 

As  to  quality  a  directive  process  may  be  homogeneous  or  hetero- 
geneous either  as  to  material,  directors,  or  form.  It  may  also  be 
continuous  or  discontinuous.  An  important  case  of  heterogeneous 
directive  is  that  in  which  the  result  is  noticeably  different  in  some 
respect  from  the  datum,  as  when  carbon  is  converted  into  diamonds, 
heat  into  light,  or  the  useless  into  the  useful. 

Directive  in  the  Form  of  Inaction 

Another  important  species  of  directive  is  that  which  may  be 
termed  negative.  This  consists  essentially  of  absence  (in  whole  or 
part)  of  action  on  the  part  of  the  agent,  or  in  his  motion  away  from 
an  object,  or  in  his  keeping  an  object  from  motion,  while  at  the 
same  time  some  other  process  which  in  the  end  will  prove  beneficial 
is  allowed  to  go  on.  Special  cases  of  negative  directive  are  inaction, 
patience,  persistence,  removal,  prevention,  rejection,  withdrawal, 
self-sacrifice,  restraint.  The  utility  of  negative  directive  is  illus- 
trated by  Napoleon's  maxim  never  to  disturb  an  enemy  while  he  is 
making  a  false  move,  by  the  frequent  success  of  what  is  called  the 
Fabian  policy,  and  by  all  cases  of  the  removal  of  waste. 

Grouped  Directive  Acts 

It  is  often  advantageous  to  perform  directive  acts  in  groups. 
Thus  in  a  well  organized  shop  by  pulling  a  single  lever  many 
machines  may  be  set  in  operation  simultaneously.  A  case  of  unit 
and  multiplier  directive  is  that  of  changing  the  course  of  an  entire 
vessel  by  a  movement  of  the  rudder  only.  Also  when  a  ship  is 
steered  in  the  region  of  a  favorable  trade  wind,  owing  to  the  con- 
tinued action  of  the  wind  the  initial  directive  act  receives  a  multiplier 
of  still  higher  order.  When  a  gun  is  fired  the  directive  work  of 
aiming  the  gun  and  pulling  the  trigger  is  multiplied  in  complex  ways. 


196  SOURCES  OF  EFFICIENCY 

It  is  even  more  advantageous  to  combine  directive  acts  in  multi- 
plicative group  systems.  An  important  case  is  that  of  superintending 
a  group  of  persons  each  of  whom  exercises  directive  functions  over 
a  group  of  other  persons  and  so  on.  Illustrations  are  the  super- 
vision and  direction  of  an  army  by  a  general,  of  a  railroad  by  its 
head,  and  of  the  government  and  people  of  the  United  States  by 
its  president. 

Other  less  homogeneous  cases  of  multiplicative  group  directive 
are  the  work  of  irrigating  a  large  tract  of  land,  or  the  shaping  of 
public  opinion  by  means  of  a  variety  of  agencifes. 

Directive  Acts  of  High  Order 

It  is  an  important  aid  to  efficiency  to  be  able  to  recognize  a 
given  directive  act  or  process  as  of  high  or  low  order,  and 
more  important  still  to  be  able  to  determine  its  exact  place  in  a 
given  scale.  In  such  a  determination  various  factors  must  be  con- 
sidered. Thus  an  act  may  be  of  high  order  if  it  moves  highly 
efficient  material,  as  the  germs,  sources,  or  underlying  causes  of 
things,  or  if  it  influences  leading  or  governing  men.  This  kind  of 
directive  is  recognized  in  the  proverb,  the  hand  that  rocks  the  cradle 
moves  the  world. 

A  case  of  somewhat  different  kind  is  the  control  of  the  business 
of  a  country  maintained  by  means  of  a  domination  of  its  transporta- 
tion routes. 

A  more  abstract  case  and  often  a  very  useful  one  is  directive  of 
the  marks  or  symbols  which  represent  objects  instead  of  the  objects 
themselves. 

Highly  efficient  directive  is  also  often  obtained  by  moving  an 
object  to  an  apex  or  controlling  point  in  a  system  or  domain.  Thus  the 
dog  jumps  at  the  throat  of  his  victim,  and  the  bee  tries  to  sting  the 
eye.  Von  Moltke  went  from  Denmark  to  Berlin  in  order  to  practise 
the  art  of  war.  Jesus  went  to  Jerusalem  that  he  might  the  better 
influence  the  religious  thought  and  practice  of  the  world. 

Other  directive  acts  of  high  order  are  those  of  converting  what  is 
harmful  or  useless  into  what  is  valuable.  On  this  same  plane  of 
high  efficiency  are  directive  acts  which  cost  little  or  no  effort,  ex- 
amples being  negative  directive  and  results  obtained  by  unconscious 
influence.  Acts  which  proceed  in  an  automatic  or  self -regulating 
way  are  of  the  same  high  grade.    In  such  cases  we  are  often  utiliz- 


DIRECTIVE  ■  197 

ing  work  done  by  other  men  at  some  distant  time  or  place  or  in 
some  obscure  way. 

On  the  highest  plane  of  all  perhaps  are  directive  acts  which  produce 
groups  or  other  fundamental  efficiency  machinery  of  some  kind. 
Several  of  the  above  elements  of  high  efficiency  may  of  course  be 
present  in  a  single  act  or  process. 

From  the  preceding  discussion  it  follows  that  directive  acts  in  a 
given  department  may  often  be  arranged  as  a  multiplicative  series. 
Thus  in  military  evolutions  we  have  tactics  and  strategy,  the  terms 
being  placed  in  ascending  order.  In  like  order  in  agriculture  are 
found  the  cultivation  of  nearby  and  familiar  plants ;  the  search  for 
and  cultivation  of  the  best  existing  plants  to  be  found  anywhere  in 
the  world ;  and  the  breeding  of  new  and  better  species  of  plants. 

In  work  in  general  we  have  as  a  multiplicative  series,  imitation, 
invention  (or  discovery),  creation. 

Indirect  Management 

With  respect  to  externality  directive  acts  may  be  characterized 
as  direct  or  indirect.  An  example  of  indirect  directive  is  the  removal 
of  an  obstacle  in  order  that  another  object  may  be  moved.  A  still 
more  indirect  case  is  that  of  undermining  an  obstacle  in  order  to 
remove  it. 

Another  form  of  indirect  directive  is  that  of  moving  an  object  by 
means  of  power  exerted  through  some  auxiliary  object,  as  when  a 
man  moves  himself  by  moving  the  locomotive  on  which  he  is  stand- 
ing, or  by  attaching  a  weight  to  a  window  sash  utilizes  at  a  later  time 
(when  raising  the  sash)  the  energy  generated  by  the  falling  of  the 
sash.  Another  form  of  directive  characterized  by  externality  is 
work  performed  on  a  large  scale. 

Complex  Species  of  Directive 

Evidently  the  above  species  of  directive  may  be  compounded  and 
complexed  in  many  ways.  Examples  of  complex  directive  are  any 
comprehensive  piece  of  engineering,  the  directive  processes  involved 
in  agriculture,  or  in  the  manufacture  of  various  articles,  in  education, 
or  in  the  various  departments  of  life  and  work  in  a  highly  civilized 
community.  Plainly  the  work  of  the  so-called  efficiency  engineer, 
when  fully  developed,  is  not  only  of  far-reaching  importance  but  of 
cumulative  complexity. 


198  SOURCES  OF  EFFICIENCY 

EFFICIENCY  RESULTS  OF  DIRECTIVE  ACTION 

General  Illustrations  of  Uses  of  Directive 

If  we  bake  clay  and  thereby  make  a  dish,  we  perform  a  directive 
act  which  has  a  variety  of  advantageous  results.  One  result  is  the 
separation  of  the  moisture  from  the  clay  (diversity),  with  the  con- 
sequence that  the  dish  may  be  permanent  in  shape  (uniformity). 
Hence  result  other  diversities  such  as  the  separation  of  food  into 
portions  and  of  each  portion  from  the  table  and  other  contaminat- 
ing matter.  Also  the  dish  thus  formed  is  capable  of  much  reuse. 
A  still  more  general  efficiental  result  is  an  increased  refinement  in 
the  multiplicative  group  organization  of  society.  Looked  at  from 
another  point  of  view,  the  making  of  dishes  leads  to  an  improve- 
ment in  human  health,  an  increase  of  happiness,  and  often  to  pro- 
longed life.  The  latter  class  of.  results  is  however  largely 
determined  and  dominated  by  the  former,  and  primary  attention 
should  therefore  be  paid  to  the  former  class. 

A  Means  to  Group  Formations 

A  directive  act  may  result  in  the  formation  of  a  group  in  a  single 
and  direct  way,  as  when  a  useful  assemblage  of  articles  is  obtained  by 
packing  a  number  of  articles  in  a  satchel.  But  directive  acts  always 
•result  in  group  formations  in  much  more  general  and  manifold  ways. 
Thus  when  any  object  is  moved  from  position  A  to  position  B  the 
result  will  be  the  separation  of  the  moved  object  from  all  points  and 
materials  near  A,  and  also  its  greater  proximity  to  those  near  B. 
Hence  many  groups  will  be  dissolved  and  others  will  be  formed ;  or 
stating  the  matter  more  generally,  many  new  uniformities  and  diver- 
sities will  be  generated  which  will  serve  as  the  raw  material  for 
group  formations. 

It  is  also  to  be  noted  in  this  connection  that  the  selection  of  an 
article  means  the  rejection  of  all  other  articles,  and  that  the  forma- 
tion of  one  group  means  the  formation  of  an  infinite  negative  or 
matrix  group. 

Economies 

In  various  cases  the  result  of  the  above  process  is  the  formation 
of  groups  which  are  especially  efficient  in  different  ways.  Thus  im- 
portant economies  may  result.  An  example  is  the  utilization  in  gas 
engines  of  the  gases  given  off  by  a  blast  furnace  with  the  consequent 


DIRECTIVE 


199 


economy  of  fuel  in  the  factory.  When  salmon  are  left  to  propa- 
gate themselves  in  a  state  of  nature  more  than  98  per  cent  of  the 
ova  or  young  fish  are  destroyed  by  other  fish  or  by  birds.  In 
artificial  hatcheries  only  15  per  cent  are  lost.  Or  the  result  may 
take  the  form  of  a  saving  of  time.  Thus  it  is  estimated  that  Luther 
Burbank  in  the  breeding  of  new  plants  has  attained  results  in  a 
single  life  time  which,  if  left  to  the  processes  of  nature,  would  have 
required  millions  of  years. 

A  Means  to  Other  Efficients 

In  like  manner  the  gain  may  take  a  unit  and  multiplier  form. 
Thus  when  a  window  sash  is  raised  in  order  that  a  breeze  may  blow 
through  the  room,  the  work  of  raising  the  sash  may  be  said  to  be 
multiplied  by  the  breeze.  Telegraph  operators  express  a  like  result 
when  they  say  that  multiplex  telegraphy  produces  "phantom  lines" 
of  wire  on  which  messages  are  carried. 

The  application  of  forced  draft  to  a  tubular  boiler  produces  both 
a  concentration  of  motion  in  a  small  portion  of  time  (increased 
velocity)  and  also  a  concentration  of  force  in  a  small  portion  of 
matter. 

The  importance  of  the  diversity  and  uniformity  results  of  di- 
rective is  illustrated  by  chemical  analysis  and  synthesis,  and  the 
products  obtained  by  means  of  them.  Examples  are  the  artificial 
production  of  camphor,  quinine,  and  salvarsan,  the  specific  for 
syphilis.  An  important  special  form  of  uniformity  which  may 
result  from  a  directive  action  is  that  obtained  by  dovetailing  to- 
gether two  or  more  irregular  objects  so  as  to  make  one  that  is  uni- 
form in  some  way. 

The  result  of  directive  may  also  be  the  production  of  an  article 
of  a  higher  plane  of  excellence  in  an  order  of  materials  scale.  Ex- 
amples are  the  superior  qualities  of  cheese,  butter,  and  tea  obtained 
by  the  careful  manipulation  of  ferments. 

Directive  acts  or  processes  may  result  in  the  formation  of  a  new 
and  more  powerful  symbolism  or  calculus,  or  it  may  open  the  way 
to  other  directives.  Thus  the  manufacture  of  iron  supplied  iron  as 
an  aid  in  later  directive  processes.  Or  it  may  produce  new  extern- 
ality. Thus  travel  gives  breadth  of  view  and  knowledge  of  new 
auxiliaries. 


200  SOURCES  OF  EFFICIENCY 

Self-developing  Fruitage 

The  dialectic  fruitage  of  directive  is  especially  prominent.  Thus 
the  man  who  first  combined  steel  and  concrete  could  not  foresee  all 
the  advantageous  results  which  would  follow.  In  a  much  more 
fundamental  field  those  who  first  obtained  mathematical  results  by 
moving  geometric  objects  and  applying  them  to  each  other  could  not 
forecast  all  the  principles  of  geometry  which  would  be  discovered  as 
a  consequence  and  the  many  applications  of  these  in  engineering  and 
various  departments  of  science. 

In  this  connection  the  fact  is  to  be  emphasized  that  in  directive 
acts  we  are  either  dealing  with  material  objects  or  with  entities  the 
substantial  aspect  of  which  has  been  made  prominent.  Hence  the 
result  of  a  directive  act  has  that  peculiar  permanency  which  is 
characteristic  of  the  categories  of  materiality  and  substance  and 
which  often  constitutes  a  new  dimension  of  efficiency.  Actually 
performing  a  process  (as  compared  with  the  theoretical  achievement 
of  results)  also  has  a  valuable  reflex  effect  on  the  doer.  He  is 
compelled  to  realize  and  observe  limitations  in  the  world  about  him, 
and  learns  to  recognize  and  avoid  certain  common  errors.  Also 
owing  to  limitations  in  his  hands,  eyes,  and  nerves,  and  to  other 
limitations  in  his  powers  of  conscious  grasp,  and  owing  to  still 
others  in  objects,  he  must  divide  a  concrete  directive  process  into 
parts  and  perform  the  whole  as  a  linear  or  semi-linear  series  or 
group  system.  He  thus  acquires  group  neighborhood  symbolism  and 
other  habits  adapted  to  the  efficient  manipulation  of  such  a  series. 
With  practice  these  powers  in  time  often  become  so  well  disci- 
plined that  they  adjust  themselves  to  given  conditions  more  or  less 
automatically. 

Transcendent  Results 

Many  of  the  results  obtained  by  the  directive  method  are  absolute 
or  infinite  in  the  sense  that  in  value  they  immeasurably  exceed  the 
data  employed.  In  a  sense  also  they  are  transcendent  in  that  they 
cannot  be  analyzed  so  as  to  be  statable  in  terms  of  the  data  or  of 
other  Efficients.  Also  some  of  them  are  unique  in  that  they  cannot 
apparently  be  obtained  without  the  use  or  aid  of  directive. 

As  illustrations  we  have  the  saving  of  life  by  the  directive  use  of 
mosquito  netting  to  exclude  the  malaria  carrying  mosquito;  or  by 
the  use  of  antiseptic  surgery;  and  the  making  visible  of  otherwise 


DIRECTIVE  20I 

invisible  objects  by  the  invention  of  the  microscope  and  telescope. 
A  further  illustration  is  the  artificial  fertilization  of  the  eggs  of 
certain  species  of  animals  by  the  use  of  chemicals,  or  even  by  the 
prick  of  a  needle. 

Hence  many  directive  acts  become  in  effect  what  may  be  termed 
acts  of  creation.  Thus  Watt  for  efficiency  purposes  created  the 
steam  engine.  Afterward  the  use  of  the  steam  engine  gave  coal  most 
of  its  value.  So  lignite  which  when  burned  directly  is  relatively 
worthless  becomes  valuable  by  being  converted  into  gas. 

Special  Fruitage  of  Each  Species  of  Directive 

Each  particular  species  of  directive  action  has  its  own  peculiar 
efficiency  functions  in  addition  to  many  of  the  more  general  ones 
given  in  the  preceding  discussion.  One  of  the  most  important 
forms  of  directive  in  this  respect  is  the  species  termed  initiative. 
An  act  of  this  kind  gives  a  certain  priority  in  time  to  one's  work 
and  this  priority  often  means  an  inclusiveness  or  groupism  which  ulti- 
mately leads  to  many  valuable  results.  Initiative  also  means  a  break- 
ing into  new  ground  and  hence  a  new  diversity,  often  a  new  unit, 
radically  new  externality,  and  other  efficiency  materials  or  results. 

Advantages  of  Management  in  Each  Department  of  Life 

An  important  way  in  which  to  realize  the  vast  amount  of  fruitage 
already  obtained  by  the  use  of  the  directive  principle,  as  well  as  to 
appreciate  the  complex  forms  in  which  these  fruits  appear,  is  to  try 
to  grasp  the  results  from  this  source  in  each  department  of  life  and 
activity.  For  instance  the  value  of  directive  in  agriculture  may  be 
realized  in  a  general  way  by  raising  the  question  as  to  what  would 
be  left  of  this  department  of  activity  if  all  directive  were  eliminated 
from  it.  In  manufacturing  it  is  estimated  that  the  one  'form  of  $-■ 
directive  called  scientific  management,  alone  has  doubled  the  output 
obtained  from  a  given  number  of  workmen  in  establishments  where 
it  is  used.  A  more  comprehensive  way  of  realizing  the  sum  total 
of  the  values  of  directive  is  to  note  that  human  progress  throughout 
has  been  marked  by  an  increasing  amount  and  progressively  higher  , 
order  of  management.  For  instance  each  epoch  of  history  has  been 
a  new  epoch  in  directive  processes,  examples  being  the  periods 
marked  by  man's  control  of  stone,  wood,  organs  of  speech,  iron, 
fire,  and  electricity. 


202  SOURCES  OF  EFFICIENCY 

Looking  at  the  matter  from  another  point  of  view  it  has  been 
stated  as  a  law  that  "other  things  being  equal,  progress  is  in  propor- 
tion to  control".  Thus  man's  control  in  the  fields  of  chemistry  and 
physics  being  greater,  progress  in  these  sciences  has  been  much 
more  rapid  than  in  botany,  zoology,  psychology,  and  sociology. 
Similarly  the  supremacy  of  the  Anglo-Saxon  in  the  world's  civiliza- 
tion at  the  present  time  is  largely  due  to  the  great  energy  which  is 
characteristic  of  this  race,  and  which  is  especially  noticeable  when 
contrasted  with  oriental  fatalism. 

Words  Illustrating  Value  of  Directive 

In  grasping  the  efficiency  importance  of  the  directive  principle,  it 
is  also  an  aid  to  note  the  values  connected  with  certain  special  and 
relatively  familiar  species  of  directive  as  analysis,  synthesis,  substi- 
tution, utilization,  management,  engineering,  superintendence,  trade, 
exchange,  control,  and  executive  work  in  all  forms. 

The  increasing  employment  of  directive  and  the  growing  appre- 
ciation of  its  value  are  indicated  by  the  increasing  use  of  such 
terms  as  social  engineer,  educational  engineer,  light,  chemical,  or 
efficiency  engineer. 

Limitations  to  Utilities  in  Directive 

Certain  limitations  in  the  fruitage  of  directive  acts  arise  from 
man's  circumscribed  control  of  objects.  Illustrations  are  man's  ina- 
bility to  cause  rain  in  the  time  of  droughts,  or  to  compel  a  horse  to 
drink  though  we  can  lead  him  to  the  water. 

The  direct  losses  connected  with  cases  of  directive  take  two 
principal  forms,  thus  we  have 

( I )  Unconscious  or  unintentional  losses,  such  as  are  indicated  by 
words  like  mistake,  and  often  also  by  the  words  misdirect,  misuse, 
misapply. 

Illustrations  are  the  mistakes  made  in  introducing  the  gipsy  moth 
and  the  English  sparrow  into  the  United  States,  and  wholly  uncon- 
scious errors  like  that  of  transporting  the  phylloxera  to  France  and 
the  Hessian  fly  to  Great  Britain. 

Losses  of  this  class  may  take  many  special  individual  specific 
forms,  such  as  excessive  directive  (as  in  meddling,  domineering, 
etc.)  ;  or  too  small  an  amount  of  directive;  or  in  directive  of  a  low 


DIRECTIVE  203 

order,  where  a  high  order  is  possible,  as  in  the  use  of  war  instead  of 
arbitration. 

(2)  The  second  important  form  of  evils  connected  with  directive 
are  conscious  and  intentional  misuse  and  misdirection,  as  in  swind- 
ling, cheating,  corrupting,  and  similar  acts  and  processes. 

Often  classes  (i)  and  (2)  are  combined  in  cases  which  are 
difficult  precisely  to  analyze,  as  in  many  forms  of  sin  and  crime. 

The  Hand  of  Efficiency 

However  after  full  allowance  for  all  limitations  and  drawbacks 
has  been  made,  we  still  find  a  high  surplusage  of  value  in  directive 
acts  and  processes.  This  we  may  sum  up  in  the  statement  that  just 
as  symbolism  is  the  tongue  of  efficiency,  so  directive  is  the  hand  of 
efficiency. 


EFFICIENCY    ANALYSIS 

From  the  preceding  discussion  it  follows  that  directive  is  essen- 
tially a  group-making  process,  but  that  it  is  this  process  considered 
from  a  peculiar  and  limited  point  of  view. 

Directive  as  a  Group-making  Process 

Thus  as  compared  with  reuse  ( i )  in  directive  special  attention  is 
paid  to  the  beginning  or  incipiency  of  group  formation,  the  process 
of  use  and  the  matter  of  results  being  often  left  in  the  background 
for  the  time  being: 

(2)  Directive  also,  to  a  greater  extent  than  reuse,  implies  or  is 
exerted  in  opposition  to  resisting  forces  or  conditions; 

(3)  Hence  directive  lays  emphasis  on  personality  and  especially 
on  the  will  exerted  in  overcoming  difficulties.  Hence  courage,  per- 
severance, knowledge  of  human  nature  and  similar  qualities  are 
specifically  prominent  in  executive  work  as  compared  with  other 
group  work. 

In  other  words  directive  is  the  group-making  process  considered  J.-- 
from  the  incipient,  concrete,  subjective  side. 

In  this  separation  of  the  directive  part  from  the  rest  of  the  group- 
making  process,  the  principle  of  diversity  is  utilized.  This  has  the 
advantage  of  making  it  possible  to  group  these  new  incipiencies  and 
treat  them  in  various  efficient  ways  as  by  applying  externalities  to 


204  SOURCES  OF  EFFICIENCY 

them.     Hence  in  the  end  it  adds  greatly  to  the  efficiency  of  the 
group  principle  in  its  various  forms. 

Other  Elements  in  Directive 

Certain  other  special  sources  of  efficiency  in  directive  should  also 
be  mentioned. 

For  instance,  motion  implies  space,  and  a  knowledge  of  the 
properties  of  space,  especially  of  its  efficiency  properties,  is  often  a 
source  of  power  in  carrying  on  directive  processes. 

Similarly  it  is  important  to  recognize  that  directive  implies  time 
in  the  general  way  in  which  all  motion  implies  it,  and  also  in  the 
special  way  indicated  by  the  word  incipiency. 

Limitation  is  also  present  in  the  form  of  opposing  forces  or  condi- 
tions. Hence  a  knowledge  of  force  and  limitation  may  be  a  source 
of  added  efficiency  in  directive  processes. 

Unique  Element 

Also  there  is  present  in  directive  a  unique  element,  not  statable, 
in  terms  of  the  other  Efficients  or  categories.  This  is  present  par- 
ticularly in  the  ethelistic  element  involved  in  directive.  We  glimpse 
this  element  in  the  power  which  living  matter  has  to  initiate  motion, 
to  move  itself,  and  in  what  we  call  freedom  of  the  will,  all  difficult 
of  analysis,  yet  all  important  possible  sources  of  new  efficiency  at 
any  time. 

Definitions 

It  will  be  well  also  to  define  as  closely  as  we  can  certain  more  or 
less  familiar  species  of  directive  to  which  we  shall  have  occasion  to 
refer  at  times. 

Initiative  is  a  species  of  directive  in  which  the  ideas  of  incipiency 
and  usually  of  opposition  are  emphasized,  all  other  elements  being 
left  vague  and  indefinite. 

Substitution  is  the  dual  directive  act  of  removing  one  object  and 
putting  another  in  its  place. 

Utilisation  is  the  act  of  transforming  that  which  has  been  unused 
into  something  directly  useful. 


DIRECTIVE  205 

METHODS  OF  APPLICATION 

The  most  fundamental  way  in  which  to  utilize  directive  to  the 
utmost  as  a  source  of  efficiency  is  to  realize  and  apply  the  fact  that 
directive  is  essentially  groupish  and  multiplicative  in  nature.  Many 
details  of  this  method  suggest  themselves  at  once  as  a  result  of  the 
preceding  discussion,  but  particular  mention  may  be  made  of  the 
following. 

The  Multiplicative  Principle  an  Aid  in  Many  Ways 

The  multiplicative  aspect  of  the  matter  is  helpful  in  realizing  the 
great  variety  of  objects  or  entities  which  may  be  directed,  the  many 
different  routes  and  ways  in  which  they  may  be  moved,  and  also  in 
holding  all  these  data  in  mind  in  a  panoramic  form  in  readiness  for 
use  as  opportunity  may  arise.  This  principle  also  enables  us  to 
realize  and  anticipate  the  extreme  power  and  extraordinary  results 
of  directive  action  in  its  developed  forms.  It  should  also  cause  us 
to  keep  in  mind  the  possibly  great  destructiveness  of  unwise  direc- 
tive. Any  artificial  method  of  work,  even  that  of  the  cultivation  of 
plants,  particularly  on  a  large  scale,  is  exposed  to  great  dangers 
since  as  some  one  has  said  such  a  process  upsets  the  balance  of 
nature.  In  other  words,  in  all  directive  work  the  universe  is  to  be 
regarded  as  in  an  almost  even  balance  between  gigantic  opposed 
multiplicative  systems,  and  hence  as  composed  of  enormous  oppor- 
tunities and  of  equally  great  dangers. 

Adaptation  to  Special  Situations 

In  certain  situations  careful  study  needs  to  be  made  in  order  to 
determine  the  most  efficient  available  species  of  directive  action.  In 
some  cases  only  vague  directive  such  as  merely  breaking  up  or 
shaking  up  a  situation  is  possible,  more  definite  action  being  post- 
poned till  the  immediate  results  of  such  incipient  action  become 
apparent.  Another  limited  form  of  action  is  that  which  is  implied 
in  the  injunction  to  cast  one's  bread  upon  the  waters.  Among  the 
most  important  but  most  difficult  species  of  directive  are  those  in- 
volved in  the  management  of  other  workers,  in  the  full  utilization  of 
the  power  peculiar  to  each  individual,  in  eugenics,  and  in  the  equit- 
able distribution  of  the  profits  of  modern  methods  of  work.  Knowl- 
edge not  only  of  the  general  principles  of  efficiency  but  of  a  great 
variety  of  technical  facts  is  called  for  in  dealing  with  such  problems. 


2o6  SOURCES  OF  EFFICIENCY 

Certain  cases  of  definite,  stubborn,  and  wide-spread  limitation, 
such  as  the  fact  that  sunshine  reaches  the  earth  in  a  scattered 
diffused  form,  must  often  be  dealt  with  in  a  number  of  different 
directive  processes.  The  investigation  of  methods  of  meeting  such 
cases  takes  the  form  of  a  study  of  sciences  like  physics,  chemistry, 
and  agriculture.  Similarly  a  knowledge  of  the  special  limitations 
and  possibilities  of  reciprocal  directive,  as  in  exchange  and  com- 
merce, requires  a  knowledge  of  the  technical  facts  and  laws  of 
psychology  and  sociology. 

Relations  of  Action  and  Inaction 

In  this  connection  attention  should  be  called  to  the  importance  of 
studying  the  relation  of  negative  directive  (or  inaction)  to  positive 
directive  processes.  Efficiency  is  often  gained  by  knowing  laws  of 
limitation  and  the  peculiarities  of  special  situations  well  enough  to 
be  able  to  determine  when  to  apply  active  directive  and  when  to 
leave  matters  to  the  dialectic  processes  of  nature.  Often  it  is  best 
to  use  these  two  methods  in  alternate  succession.  As  an  illustration 
we  have  the  fact  that  it  is  often  a  source  of  efficiency  not  to  try  at 
first  to  make  one's  work  too  finished  and  complete,  but  to  leave 
something  to  the  self-developing  power  of  circumstances,  and  later 
to  apply  methods  of  correction  and  adjustment. 

A  special  form  of  combined  positive  and  negative  directive  work- 
is  that  in  which  the  directive  process  has  in  large  part  become  auto- 
matic and  self-regulative.  As  has  been  pointed  out  elsewhere  such 
forms  are  of  a  high  order  of  efficiency. 

Superiority  of  Constructive  Work 

Particular  attention  should  also  be  called  to  the  fact  that  in 
directive  processes  constructive  work  should  always  if  possible  be 
dominant,  and  destructive  work  such  as  punishment  and  surgery, 
incidental  and  secondary.  This  principle  constitutes  a  directive  of 
directive  in  that  it  is  a  directive  of  the  highest  species  of  this 
efficiency  instrument  to  the  first  place. 

Externality  as  an  Aid  in  Directive 

All  kinds  of  externality  are  particularly  useful  in  directive  pro- 
cesses but  especial  mention  may  be  made  of  the  freedom  and  scope 
given  to  directive  methods  by  using  abstract  externality  in  the  form 
of  a  broad  view  of  things. 


DIRECTIVE 


207 


In  particular  many  efficiency  processes  should  be  organized  so  as  to 
produce  not  only  the  result  immediately  called  for  but  also  a  surplus, 
often  a  continuous  stream  of  results,  and  arrangements  made  to 
direct  this  surplus  to  the  apices  of  other  efficiency  processes. 

Ideal  Species 

In  general  the  entire  body  of  the  Efficients  when  organized  to- 
gether form  the  most  powerful  and  comprehensive  of  all  aids  in 
directive  work.  Or  to  state  the  matter  in  a  still  more  general  way 
the  ideal  form  of  the  instrument  under  consideration  is  the  directive 
of  efficiental  data  in  efficiental  ways  for  efficiental  ends. 

Recapitulation  of  Chapter 

To  sum  up  the  chapter,  one  of  the  most  obvious  methods  of  ob- 
taining better  results  in  any  situation  is  that  of  directive  action  or 
management.  Simple  as  this  method  often  seems,  it  nevertheless, 
needs  careful  analysis  and  study  in  order  to  realize  even  its  main 
efficiency  possibilities. 

Species  of  management  may  be  classified  according  to  the  various 
kinds  of  material  moved,  or  according  to  the  various  agencies  which 
move  objects,  or  with  respect  to  the  ways  in  which  objects  may  be 
moved,  or  according  to  the  various  results  aimed  at.  Individual 
mention  may  be  made  of  such  special  forms  as  inaction,  initiative, 
and  indirect  management. 

Directive  action  not  only  has  such  palpable  uses  as  the  utilization 
of  otherwise  unused  materials  and  the  prevention  of  various  kinds 
of  waste,  but  it  also  has  the  more  fundamental  value  of  leading  to 
the  formation  of  groups,  systems,  and  various  other  Efficients,  and 
hence  to  the  efficiency  results  characteristic  of  each  of  these.  In  a 
peculiar  sense  it  thus  leads  to  self-developing  results  and  often  to 
transcendent  fruitage.  Each  special  kind  of  directive  produces  its 
own  peculiar  efficiency  results.  Hence  also  directive  finds  a  special 
field  of  application  in  each  department  of  life. 

The  same  general  principles  which  have  been  laid  down  in  pre- 
vious chapters  as  to  the  best  methods  of  using  other  Efficients,  ap- 
ply also  to  directive.  In  addition,  special  attention  is  here  called  to 
the  importance  of  a  careful  study  of  action  and  inaction  in  any 
field  of  operations,  and  also  to  the  desirability  of  making  con- 
structive processes  as  dominant  as  possible  over  those  which  are 
destructive. 


208  SOURCES  OF  EFFICIENCY 


EXERCISE  12 


State  the  class  or  classes  of  directive  action  to  which  each  of  the  following 
instances  belongs: 

1.  Winding  up  a  watch  4.  The  manufacture  of  shoes 

2.  Pruning  a  tree  5.  The  choice  of  one  of  two  objects 

3.  Vaccination  6.  Physical  exercise 

7.  Use  of  lieutenants. 

8.  Exchange  of  goods  with  a  foreign  country. 

9.  Changing  the  direction  of  a  moving  object. 

10.  Directing  sheep  by  directing  their  leader. 

11.  The  use  of  a  furnace  with  a  thermostat  attached. 

12.  Introduction  of  the  gipsy  moth  into  the  United  States. 

13.  Making  a  woman's  hat  out  of  parts  of  old  hats. 

14.  Damming  of  the   Mississippi   River   and   generation    of   electricity   by 
the  water  power  thus  made  available. 

State  as  many  as  you  can  of  the  different  kinds  of  directive  involved  in 
the  work  of  a 

15.  Farmer  17.  Editor  of  a  paper    19.  Manager  of  a  factory 

16.  Teacher         18.  Sculptor  20.  President  of  the  United  States 

Give  two  examples  of  each  of  the  following  species  of  directive  action : 

21.  Imitation  26.  Heterogeneous  31.  Of  high   order 

22.  Prophetic  2^.  Negative  32,  Indirect 

23.  Indefinite  28.  Grouped  ZZ-  Substitution 

24.  Reciprocal  29.  Multiplicatively  grouped      34.  Utilization 

25.  Homogeneous        30.  Of  low  order  35.  Exchange 

36.  Complex 
ZT.  Give  a  multiplicative  series  of  methods  of  starting  a  fire. 

38.  State  in  what  ways  a  mountain  may,  in  effect,  be  removed  by  man. 

39.  Point  out  the  elements   of   directive  in   the  use  of  a   fireless   cooker 
and  the  advantages  which  result. 

40.  Give  an  example  of  a  process  of  directive  which  has  been  cumulatively 
complex  in  its  development, 

41.  State,  as  far  as  possible  in  efficiental  terms,  the  advantageous  results 
of  each  of  the  cases  of  directive  mentioned  in  Exs.  1-14. 

Give  an  instance  in  which  an  important  result  of  the  following  kind  has 
been  obtained  by  the  use  of  directive: 

42.  An  economy  of  force  47.  Of  a  diversity 

43.  An  economy  of  time  48.  The  saving  of  life 

44.  A  concentration  of  force  49.  An  externality 

45.  Formation  of  a  group  50.  A   loss 

46.  Of  a  uniformity  51  •  Self-developing  results 

52.  Point  out  the  advantages  and  the  disadvantages  in  carrying  a  number 
of  keys  on  one  ring. 

53.  Give  an  example  where  intense  heat  is  obtained  by  a  directive  process. 

54.  Also  one  where  intense  light  is  thus  obtained. 


DIRECTIVE 


209 


55.  Discuss  the  principles  of  directive  involved  in  a  use  of  a  portable 
saw  mill. 

56.  Also  in  making  and  using  an  artesian  well. 

57.  State  the  different  kinds  of  directive  action  involved  in  transforming 
an  object. 

58.  Give  an  example  in  which  the  efficiency  of  a  directive  process  is  in- 
creased by  the  use  of  diversity. 

59.  By  use   of  uniformity. 

Give  two  examples  in  which  directive  action  is  restricted  in  itself  or  in 
its   results   by   limitations    in  : 

60.  Objects  61.  Directors 

62.  Give  some  of  the  advantages  which  result  from  the  use  of  artificial 
light. 

63.  Give  two  examples  where  a  directive  process  has  been  aided  (or 
might  be  improved)  by  the  use  of  an  improvised  symbolism. 

64.  Give  an  example  of  a  directive  process  which  has  been  improved  by 
being  made  at  least  partly  automatic. 

65.  State  the  advantages  of  having  the  reserve  of  supplies  in  a  factory 
kept  up  automatically  by  the  use  of  a  predetermined  maximum  and  minimum. 

66.  Give  an  illustration  of  the  value  of  partial  or  entire  inaction  with 
reference  to  a  given  process. 

67.  Give  an  instance  where  action  and  inaction  are  combined  advantage- 
ously in  alternate  succession. 

68.  Discuss  the  advantages  which  result  from  the  fact  that  man  is  now 
able  to  transport  live  fish  from  any  one  part  of  the  inhabited  world  to  any 
other  part. 

69.  State  the  ways  in  which  a  wide  knowledge  of  the  state  of  the  market 
for  any  given  article  aids  in  the  <listribution  and  sale  of  the  article. 

70.  Why  is  it  often  more  advantageous  to  move  a  threshing  machine  to 
wheat  stacks  rather  than  to  move  the  stacks  to  the  machine?  Give  two 
other  illustrations  of  efficiency  obtained  by  the  directive  method  here  involved. 

71.  Discuss  will  power  as  an  element  of  success. 


CHAPTER  XII 
KINEMATIC  AND  DYNAMIC 
Illustrations 

At  the  conference  on  Scientific  Management  held  at  Dartmouth 
College  in  the  year  191 1,  an  efficiency  engineer  stated  that  in  a  cer- 
tain factory  which  he  had  been  called  on  to  inspect,  he  had  found  one 
machine  whose  speed  he  was  able  to  increase  forty-four  fold.  In- 
creasing the  speed  of  a  machine  in  this  way  evidently  meant  that 
the  capital  invested  in  the  machine  and  the  wages  of  the  workman 
operating  it  were  both  made  44  times  as  productive  as  before  and 
meant  also  an  increase  in  efficiency  in  the  whole  establishment  in 
other  ways. 

On  another  occasion  an  analytic  examination  of  the  work  of  a 
bricklayer  showed  that  the  workman  in  laying  a  brick  was  making 
18  distinct  motions  such  as  stooping  down  to  pick  up  a  brick,  lifting 
it,  turning  it  over  to  examine  it  on  all  sides,  etc. ;  that  this  number 
of  motions  might  be  reduced  to  5 ;  and  that  in  this  way  the  number 
of  bricks  laid  by  the  workman  in  one  hour  could  thus  be  increased 
from  120  to  350.  In  this  case  the  motions  made  by  a  workman  in  a 
given  operation  constituted  a  convenient  symbol  for  the  energy  and 
time  expended  by  him,  and  a  convenient  means  by  which  to  study 
and  increase  the  degree  of  efficiency  in  his  work.  These  illustrations 
show  how  the  study  of  motions  as  such  may  be  an  important  source 
of  efficiency. 

Again  man  in  propelling  a  canoe  by  a  paddle  necessarily  expends 
considerable  muscular  energy.  When  for  this  muscular  power  some 
prehistoric  savage  substituted  wind  energy  applied  by  means  of  a 
sail,  he  adopted  an  efficiency  process  of  the  first  importance,  viz. :  the 
utilization  by  man  of  the  forces  and  motions  in  the  external  world. 
For  such  utilization  not  only  means  an  economy  of  human  energy 
and  the  employment  in  higher  fields  of  the  power  thus  saved,  but 
also  greater  velocity,  larger  and  more  concentrated  masses  of 
energy,  and  power  in  more  manageable  form.  The  instance  just 
given  illustrates  the  fact  that  the  study  of  force  as  such,  particularly 
forces  in  the  outside  world,  may  be  an  important  source  of  efficiency 
to  man. 

210 


KINEMATIC  AND  DYNAMIC  211 

General  Statement 

Hence  it  will  be  a  prime  source  of  efficiency  temporarily  to  isolate 
motion,  speed,  and  force  as  a  related  group,  to  objectify  them,  and 
to  concentrate  attention  upon  them  with  a  view  to  developing  them 
to  the  utmost  as  factors  in  obtaining  results. 

At  the  outset  it  will  be  convenient  to  observe  that  motion  for  our 
purpose  means  necessarily  a  regrouping  in  several  ways ;  that  speed 
means  a  concentration  of  motion  with  respect  to  time;  and  that 
force  is  a  useful  externality  or  handle  by  which  to  control  motion 
and  its  results.  It  is  difficult  to  discriminate  a  motion  in  all  cases 
from  the  force  or  forces  connected  with  it.  But  in  many  instances  it 
will  be  an  aid  in  obtaining  the  utmost  efficiency  from  the  categories  in 
hand,  to  treat  as  more  or  less  pure  or  independent,  those  motions 
where  the  forces  involved  are  small  or  obscure,  as  well  as  those 
which  are  logically  separable  from  the  forces  producing  them. 

CLASSIFICATION  OF  MOTIONS 
Classification  of  Objects  which  move 

Motions  may  be  classified  by  grouping  them  according  to  the 
objects  which  move.  Thus  we  may  have  motions  of  organic  or 
inorganic  objects;  of  large,  small,  light,  or  heavy  objects;  of  mater- 
ial things ;  or  of  ideal  entities.  Illustrations  of  the  last  class  named 
are  the  growth  of  a  reputation,  spread  of  an  idea,  or  a  motion  like 
that  recognized  in  the  phrase,  quick  as  thought. 

In  this  connection  it  is  to  be  noted  that  all  directed  objects  (see 
the  preceding  chapter)  are  in  a  state  of  motion  but  that  many  other 
motions  are,  for  the  present  at  least  and  in  certain  ways,  best  treated 
as  independent  of  any  directing  power.  As  examples  of  the  latter 
class  we  have  the  motions  of  the  atoms  in  a  molecule  and  of  the 
solar  system  through  space,  and  a  host  of  motions  intermediate 
between  these  two  in  some  respect. 

It  should  also  be  observed  that  every  object  moves  in  some  way 
or  ways  but  not  in  all  ways.  Hence  we  have  the  general  statement, 
useful  at  least  as  a  first  approximation,  that  motion  is  the  normal 
state  of  the  universe,  and  that  any  state  of  apparent  rest  is  a  case 
of  motions  which  cancel  each  in  some  respect. 


212  SOURCES  OF  EFFICIENCY 

Classification  of  Forms  of  Motion 

Motions  may  also  be  classified  according  to  their  forms  or  other 
abstract  individualizing  qualities.  In  this  respect  the  different 
species  of  directive  given  in  the  preceding  chapter  are  also  different 
cases  of  motion.  But  owing  to  the  peculiarities  of  motion  and  force 
as  sources  of  efficiency  when  considered  independently  of  human 
originating  power,  certain  of  these  species  become  of  such  peculiar 
importance  as  to  be  worthy  of  special  mention.  To  this  list  some 
new  species  should  also  be  added. 

For  instance  particular  mention  may  be  made  of  wave  or  alter- 
nating motion.  This  species  is  of  such  importance  that  it  will  be 
treated  at  length  in  a  separate  chapter  (see  p.  230). 

It  is  also  important  to  note  that  spatially  all  motions  may  be 
regarded  as  compounded  of  two  fundamental  species,  viz. :  motions 
of  translation  and  motions  of  rotation. 

Attention  should  also  be  called  to  hidden  or  obscure  motions.  It 
is  sometimes  of  service  to  group  such  motions  according  to  the 
causes  which  make  them  invisible.  Among  these  causes  are  small - 
ness  of  the  moving  object,  extreme  slowness  or  quickness  of  the 
motion  involved,  great  distance  of  the  object,  intervening  opaque 
materials,  and  lack  of  color  in,  or  the  ideal  nature  of,  the  moving 
object. 

Groups  of  Motions 

Motions  may  be  classified  in  different  ways  with  reference  to  the 
group  principle.  Thus  a  resultant  motion  is  a  highly  fused  group  of 
motions. 

Of  especial  importance  are  certain  cases  of  multiplicatively 
grouped  motion.  An  instance  is  a  motion  obtained  by  gearing  a  set 
of  wheels  so  that  the  cogs  on  the  rim  of  each  wheel  act  upon  the 
cogs  on  the  hub  of  the  rest.  Such  a  system  may  be  used  to  produce 
great  velocity  as  in  the  apparatus  used  to  measure  the  velocity  of 
light,  or  to  produce  slowness  or  uniformity  as  in  the  mechanism  of 
a  clock.  Another  form  of  multiplicatively  grouped  motion  is  il- 
lustrated in  the  swinging  of  a  golf  club,  the  body  in  this  case  being 
treated  as  jointed  from  the  toes  up,  each  part  rotating  upon  the 
end  of  the  part  that  precedes  it  in  order.  Still  another  species 
under  this  general  class  is  the  combination  of  motions  embodied  in 
the  sun,  planets,  and  satellites  forming  the  solar  system. 


KINEMATIC  AND  DYNAMIC 


213 


A  case  of  multiplicatively  grouped  motion  widely  different  from 
the  preceding  is  that  of  a  propagation  of  some  sort  through  any 
genetic  multipHcative  group  system  as  the  transmission  of  a  charac- 
teristic through  several  generations  of  a  person's  descendants,  or 
that  of  the  spread  of  a  motion  from  the  apex  of  any  group  system 
throughout  all  its  suborders,  as  when  a  piece  of  information  is  con- 
veyed from  the  commanding  general  throughout  an  army. 

Motions  of  High  Order 

For  our  purpose  it  is  also  important  to  notice  that  certain  motions 
are  higher  than  others  in  what  may  be  regarded  as  an  order  of 
materials  scale.  Thus  a  motion  may  be  of  high  order  owing  to  its 
position  in  a  multiplicative  group  system  of  motion,  an  example  being 
the  motion  of  the  end  of  a  golf  club.  Another  important  case  is 
motion  of  material  of  a  high  order  even  when  the  actual  concrete 
velocity  is  small.  Thus  with  respect  to  the  progress  of  the  world, 
the  motion  of  Jesus  as  he  toiled  up  Calvary  was  immeasurably  more 
swift  than  that  of  a  driver  in  a  Roman  chariot  race. 

Complex  Motions 

The  number  of  ways  in  which  motions  may  be  combined  and 
complexed  is  without  limit.  Instances  are  the  motions  involved  in 
a  widespread  storm,  in  a  war,  or  in  a  period  of  human  progress. 

CLASSIFICATION    OF    FORCES 

For  our  purpose  it  is  useful  to  regard  forces  as  grouped  in  three 
different  ways,  viz.: 

(i)  According  to  the  substances  in  which  they  are  found  or 
contained  or  by  which  they  are  conveyed; 

(2)  According  to  the  species  of  motion  which  they  produce; 

(3)  With  respect  to  other  results  produced  by  them. 

Sources  of  Forces 

Viewed  in  the  first  of  these  ways,  particular  groups  of  forces  are 
those  obtained  from  wood,  coal,  oil,  falling  water,  gas,  winds,  nitro- 
glycerine, etc.  In  most  of  these  cases  the  sun  is  the  ultimate  source 
of  energy.  Also  certain  chemical  materials  as  radium,  are  found 
to  be  a  prime  source  of  energy.    Viewing  materials  and  substances 


214  SOURCES  OF  EFFICIENCY 

in  other  ways  we  get  other  groups  of  forces,  such  as  atomic,  molecu- 
lar, and  mass  forces;  or  those  termed  physical,  biological,  mental, 
spiritual,  and  social.  Some  of  the  highest  and  most  important  forces 
reside  in  methods,  especially  in  efficiency  processes. 

An  important  dual  grouping  of  forces  is  that  implied  in  the  terms 
organic  and  inorganic,  organic  forces  being  those  which  appear 
only  in  connection  with  organic  or  so-called  living  matter,  and  inor- 
ganic those  which  may  also  appear  in  connection  with  dead  matter. 
These  classes  have  also  been  termed  incarnate  and  uncarnate. 

In  this  connection  it  is  also  well  to  draw  a  distinction  between 
forces  which  act  apparently  by  direct  contact  of  bodies  and  those 
which,  in  appearance  at  least,  act  across  empty  space,  examples  of 
the  latter  being  gravitation,  electricity,  and  magnetism. 

Forces  Characterized  by  Motions  produced  by  them 

On  taking  up  the  second  method  of  characterizing  forces,  we 
find  that  forms  of  motion  produced  by  forces  have  already  been  de- 
scribed. But  often  when  forces  and  motions  are  considered  together 
in  this  way,  individual  species  of  force  of  especial  importance  arise. 
An  instance  is  the  classification  of  winds  as  local,  continental,  or 
planetary. 

In  this  connection  particular  attention  may  also  be  called  to  the 
multiplicative  grouping  of  forces  and  to  forces  of  various  orders  in 
a  multiplicative  scale. 

Forces  Characterized  by  other  Effects 

In  classifying  forces  primarily  according  to  the  results  produced 
by  them  (other  than  motions  pure  and  simple)  we  have  for  example 
forces  of  decay,  repair,  or  growth ;  attractive  forces  like  gravitation, 
chemical  cohesion,  and  magnetism,  and  repulsive  and  radiating  forces 
such  as  light,  heat,  and  magnetism. 

Mention  at  this  point  should  be  made  of  negative  and  resistant 
forces ;  also  of  mere  continuance  forces  such  as  inertia  and  momen- 
tum. Closely  connected  with  these  ideas  is  a  classification  of  forces 
according  to  the  degree  of  human  control  of  which  they  are  capable. 

Forces  Characterized  by  a  Combination  of  Methods 

For  some  purposes  certain  forces  are  best  characterized  by  a 
combination  of  the  above  principles  of  classification.  Thus  some 
forces,  as  we  usually  discriminate  them,  are  determined  partly  by  the 


KINEMATIC  AND  DYNAMIC  215 

material  in  which  they  are  found  incorporated,  partly  by  the  kinds 
of  motion  to  which  they  give  rise,  and  in  part  by  the  more  ultimate 
results  which  they  produce.  Examples  are  sound,  heat,  light,  elec- 
tricity and  magnetism,  elasticity,  and  chemical  affinity.  More 
abstract  cases  are  the  force  of  public  opinion,  of  publicity,  fashion, 
supply  and  demand,  etc.  Of  higher  order  still  are  the  forces  which 
produce  groups  and  the  other  Efficients,  and  also  those  which  these 
agents  exert.  The  latter  class  we  may  term  efficiental  forces.  The 
force  inherent  in  superior  efficiency  we  shall  find  to  be  the  most 
powerful  and  inclusive  of  all. 

It  is  also  necessary  to  allow  for  subtle  and  even  transcendental 
forces  as  possible  sources  either  of  added  efficiency  or  of  limitation 
and  opposition. 

Looked  at  in  their  historical  development,  especially  if  we  include 
abstract  types,  forces  have  been  cumulatively  complex  from  age  to. 
age. 

EFFICIENCY  FUNCTIONS  OF  MOTIONS  AND  SPEED 

In  investigating  the  efficiency  meanings  and  values  of  motion,  we 
consider  three  different  cases  or  points  of  view.     These  are: 

(i)  The  efficiency  meaning  of  motion  as  such  (i.e.  when  con- 
sidered independently  of  forces)  : 

(2)  The  uses  of  motion  in  cases  where  the  forces  involved  are 
small,  obscure,  or  beyond  control; 

(3)  The  efficiency  function  of  motion  when  the  related  force  is 
considerable  in  amount,  more  or  less  evident,  and  under  control. 

Later  the  efficiency  value  of  superior  speed  will  be  considered. 

Efficiency  Value  of  Miction  in  Itself 

First,  then,  considering  motion  by  itself,  it  is  observed  that  a 
moving  point  or  object  generates  a  group  the  elements  of  which  are 
the  moving  point  or  object  in  its  various  positions.  The  group  thus 
generated  may  take  an  extreme  or  infinite  form  as  when  a  point 
generates  a  line,  or  a  line  a  surface,  and  so  on. 

It  is  to  be  noted  that  not  only  does  a  moving  object  generate  a 
group  in  the  way  mentioned  but  that  it  also,  if  its  relations  to  objects 
outside  of  its  path  be  considered,  gives  rise  to  a  continuity  of  new 
multiplicative  groupings  and  efficientizings.  For  instance,  by  trac- 
ing progressive  changes  in  organisms  we  get  the  various  unities 
which  characterize  the  processes  of  evolution. 


2i6  SOURCES  OF  EFFICIENCY 

Uses  of  Motions  Related  to  Slight  Forces 

Where  the  related  forces  are  inconsiderable,  the  following  illus- 
trations will  serve  to  make  clear  some  of  the  efficiency  values  of 
motion.  A  single  set  of  books  kept  in  rapid  circulation  will  take  the 
place  of  several  sets  each  kept  in  a  distinct  library.  By  taking 
advantage  of  the  migration  of  birds  a  person  is  saved  the  labor  of 
travelling  to  different  places  in  order  to  observe  various  species  of 
birds.  A  flower  by  utilizing  the  motion  of  the  bee  is  saved  the  labor 
of  producing  a  large  amount  of  pollen  as  a  means  to  cross  fertiliza- 
tion. An  astronomer  in  determining  the  distance  of  the  sun,  by 
taking  his  station  near  the  earth's  equator  and  utilizing  the  rotation 
of  the  earth  on  its  axis,  avoids  the  expense  of  measuring  a  large 
arc  of  the  earth's  circumference  and  taking  observations  from  each 
end  of  the  arc.  A  merchant  who  builds  a  store  on  a  city  corner 
where  many  people  are  passing  and  repassing,  is  saved  a  large 
amount  of  work  and  expense  in  looking  up  trade. 

An  important  class  of  instances  under  this  head  is  the  motion 
or  growth  of  ideal  or  mental  objects.  An  example  is  the  method  of 
proof  called  superposition  as  used  in  geometry.  A  more  general 
and  important  case  is  that  of  the  useful  results  obtained  by  the 
more  or  less  spontaneous  motion  of  ideas  among  themselves  as  in 
the  processes  of  the  imagination. 

Motion  in  several  of  the  above  instances  has  the  effect  of  giving 
efficiency  a  new  dimension.  The  new  dimension  and  also  the  dia- 
lectic of  advantages  which  sometimes  results  from  it  are  illustrated 
in  the  new  powers  conferred  by  aerial  flight,  particularly  in  war. 

Uses  of  Motions  Related  to  Considerable  Forces 

The  uses  which  may  be  made  of  motions  where  the  related  forces 
are  considerable  and  more  or  less  under  control  are  illustrated  in 
the  case  of  the  bricklayer  given  on  p.  210.  In  such  cases  not  only 
should  the  number  of  motions  be  considered,  but  also  the  duration, 
amplitude,  and  often  form  of  each.  In  general  in  such  cases  waste 
motion  is  a  symbol  for  waste  energy.  On  the  other  hand  graceful 
motion  means  highly  efficient  action.  A  somewhat  similar  utiliza- 
tion of  motion  as  a  symbol,  is  the  recognition  of  a  person  by  some 
peculiarity  of  gesture  or  gait.  A  more  important  case  is  that  of 
reading  the  signs  of  the  times,  that  is,  grasping  the  future  by  means 
of  slight  changes  in  progress  at  any  given  time. 


KINEMATIC  AND  DYNAMIC  217 

Transcendent  Values 

The  benefits  conferred  by  motion  are  often  unique  and  not  other- 
wise attainable.  Thus  the  rotation  of  the  planet  Mars  on  its  axis 
enables  us  to  observe  the  planet's  entire  surface,  a  fact  which  i^ 
more  fully  appreciated  when  we  recall  that  the  moon  by  keeping  the 
same  face  turned  toward  the  earth,  prevents  us  from  ever  seeing 
more  than  one  of  its  hemispheres.  A  more  important  case  is  that 
where  motion  saves  life. 

Another  class  of  the  extreme  or  transcendental  results  of  motion 
is  that  whereby  a  motion  or  change  beyond  what  is  termed  a  critical 
point  produces  a  radical  transformation  in  an  object.  An  illustra- 
tion is  the  fact  that  water  becomes  ice  when  its  temperature  passes 
through  the  freezing  point,  or  that  positive  quantity  becomes  nega- 
tive by  passing  through  the  zero  point.  Other  important  cases  are 
the  change  of  a  solid  into  a  liquid,  or  of  a  liquid  into  a  gas. 

Advantages  of  Speed 

The  advantages  which  often  spring  from  increased  velocity  were 
also  illustrated  in  the  opening  paragraph  of  the  chapter.  In  some 
cases  this  element  of  additional  speed  adds  what  is  in  effect  a  new 
dimension  to  efficiency.  This  is  recognized  in  the  pedagogic  precept 
first  to  learn  to  do  a  thing,  then  to  learn  to  do  it  well,  then  to  learn 
to  do  it  quickly. 

This  new  dimension  of  efficiency  may  take  certain  special  forms. 
Thus  superior  speed  in  reaching  Round  Top  at  the  battle  of  Gettys- 
burg enabled  the  Northern  army  to  win  the  battle.  So  in  competi- 
tive races  of  various  kinds  the  man  who  wins  by  even  an  inch  takes 
the  whole  prize.  This  efficiency  property  of  speed  is  recognized  in 
the  proverb,  the  early  bird  gets  the  worm.  The  fortunes  of  the 
Rothschild  family  were  greatly  advanced  by  the  fact  that  their 
London  representative  learned  the  result  of  the  Battle  of  Waterloo 
several  hours  earlier  than  any  one  else  in  the  city.  In  like  manner 
the  farmer  who  first  brings  his  crop  to  maturity  and  the  business 
man  who  first  learns  the  news  that  will  affect  the  market,  will  each 
profit  thereby. 

Superior  speed  at  one  time  or  in  one  respect  may  mean  a  whole 
group  of  similar  advantages.  For  instance  the  man  who  begins 
work  first  on  a  given  day  may  be  able  to  begin  every  enterprise 


2lB  SOURCES  OF  EFFICIENCY 

ahead  of  his  competitors  throughout  the  day.     The  same  principle 
applies  to  much  larger  periods  of  time. 

An  increase  of  velocity  or  a  superiority  in  speed  may  also  lead  to 
results  apparently  otherwise  unattainable,  or  to  results  in  some 
respect  immeasurable  in  value.  Thus  in  time  of  flood  in  a  valley, 
increased  speed  may  be  a  means  of  saving  life.  Also  the  rapidity 
with  which  plant  breeders  attain  results  enables  us  to  enjoy  results 
which  the  slower  processes  of  nature  could  not  achieve  within  our 
lifetime. 

.Complex  Fruitages 

The  above  useful  results  of  motion  and  speed  are  often  complexed 
in  various  ways.  An  instance  is  the  circulation  of  the  blood  with  the 
many  advantages  to  the  organism  which  result,  and  the  enhancement 
of  these  advantages  in  those  higher  organisms  where  the  circulation 
is  most  rapid. 

Increasing  Value  of  Motion  and  Speed 

A  comprehensive  grasp  of  the  utilities  in  motion  is  obtained  by 
observing  that  the  progressive  development  of  various  forms  of  life 
and  of  human  civilization  as  a  whole  have  alike,  as  a  rule,  been 
marked  by  an  increasing  use  of  motion  in  various  forms,  and  by  an 
increasing  speed  in  processes.  The  speed  of  the  fish  exceeds  that 
of  the  amoeba;  that  of  the  bird  exceeds  that  of  the  fish;  and  the 
telegraph  message  moves  more  swiftly  than  the  bird.  The  present 
superior  efficiency  of  certain  processes  of  manufacture  are  due  to  the 
fact  that  in  the  last  ten  years  the  average  speed  of  machine  work 
has  increased  threefold  in  the  United  States  and  that  of  metal  cut- 
ting sevenfold  where  high-speed  steel  is  used.  On  the  other  hand 
lack  of  motion,  or  of  velocity,  or  of  utilization  of  motions,  usually 
means  lack  of  power.  Hence  also  it  results  that  times  of  motions 
and  change  are  periods  of  exceptional  opportunity  for  the  capable 
personality. 

Limitations  in  the  Utility  of  Motion  and  Speed 

At  the  same  time  attention  should  be  called  to  the  fact  that  certain 
dangers  and  losses  are  connected  with  the  use  of  motion,  or  of  in- 
creased speed,  in  certain  cases.  Thus  the  danger  in  too  much 
motion  is  expressed  in  the  proverb,  a  rolling  stone  gathers  no  moss. 


KINEMATIC  AND  DYNAMIC  219 

The  loss  occasioned  by  an  excessive  dependence  on  objective  motions 
is  illustrated  by  the  limitations  of  a  clam  or  oyster  as  compared  with 
the  fish. 

Similarly  certain  natural  limitations  often  exist  with  respect  to 
speed,  and  any  energy  expended  in  trying  to  overcome  these  limita- 
tions in  direct  ways  will  be  wasted.  Also  often  when  it  is  possible 
to  increase  speed,  the  attempt  to  do  this  will  not  pay,  either  because 
of  the  large  outlay  of  energy  called  for,  or  on  account  of  the  com- 
pensating dangers  and  losses  which  result.  Illustrations  are  the  loss 
of  the  steamship  Titanic  in  April,  191 2,  or  the  evil  physical  and 
moral  effects  of  too  high  a  speeding  up  of  workmen  in  a  factory, 
or  of  too  fast  a  pace  in  any  life  process. 

Beyond  the  mere  dangers  of  misuse  of  motions,  certain  inherent 
defects  are  characteristic  of  motion  as  an  independent  phenomenon, 
the  chief  of  which  is  its  frequent  lack  of  tangible  externality  by 
which  it  may  be  controlled.  Hence  arises  the  importance  of  force  as 
an  auxiliary  efficiency  concept  in  connection  with  the  use  of  motion. 

EFFICIENCY  FUNCTIONS  OF  FORCE 

From  the  point  of  view  which  is  fundamental  in  the  present  in- 
vestigation, we  find  in  force  and  in  the  objects  in  which  forces  are 
stored  or  through  which  they  act,  efficiency  properties  of  two  princi- 
pal kinds,  viz. : 

(i)  Those  properties  which  are  an  aid  in  the  use  of  motion; 

(2)  Those  which  belong  more  distinctively  to  force  (or  energy) 
itself. 

Force  as  a  Source  of  Motion 

In  the  first  place,  in  treating  motions  by  means  of  the  objects  in 
which  are  stored  the  forces  which  produce  motions,  we  utilize  cer- 
tain permanences  which  characterize  these  objects.  Thus  the  force 
stored  in  wood,  oil,  and  coal  does  not  vary  appreciably  in  quantity 
or  form,  however  long  these  objects  are  stored.  Hence  arises  the 
possibility  of  transferring  potentialities  of  motion  (and  its  results) 
widely  in  space  and  time. 

This  adds  greatly  to  the  scope  of  directive  processes  in  space  and 
time,  to  the  possibility  of  substituting  a  cheap  source  of  motion 
for  a  costly  one,  and  to  many  other  of  the  advantages  of  a  large 
externality. 


220  SOURCES  OF  EFFICIENCY 

Also  fuel  and  some  of  the  other  force-sources  of  motion  are 
capable  of  fine  and  exact  subdivisions,  and  lead  to  certain  important 
delicacies  and  accuracies  in  motion. 

These  properties  of  the  sources  of  motion  also  make  it  possible 
to  group  multiplicatively  and  to  systematize  these  sources  and  the 
motions  which  they  produce  in  extraordinary  ways. 

Values  Peculiar  to  Forces 

Force  also  has  certain  independent  powers  in  producing  the  desira- 
ble ends  of  efficiency  processes  as  specified  in  Chapter  IX.  Thus 
heat  produces  warmth,  health,  and  hence,  in  a  measure,  life  itself. 
Light  gives  knowledge  and  externality  in  many  ways,  and  has  other 
useful  properties.  Inertia  often  means  certain  permanences  in 
time,  and  similarly  other  negative  forms  of  force  have  their  peculiar 
functions.  The  specific  and  more  or  less  concrete  uses  of  each  kind 
of  force  are  described  in  books  treating  distinctively  of  them. 

The  general  utility  of  objective  forces  as  substitutes  for  more 
costly  forms  of  human  energy  was  pointed  out  in  the  introductory 
paragraphs  of  this  chapter. 

Transcendent  Values 

We  should  not  fail  to  observe  also  that  certain  of  the  above  values 
in  some  circumstances  may  be  transcendental  or  unique.  Instances 
are  the  utilization  of  night  hours  by  the  use  of  artificial  light,  or  the 
development  of  life  by  the  aid  of  artificial  heat  in  certain  situations 
where  life  could  not  exist  otherwise.  Other  instances  are  certain 
esthetic  results,  as  when  light  in  itself  becomes  a  source  of  pleasure. 
So  various  forces  and  motions  may  give  rise  to  what  is  termed  the 
joy  of  living. 

Values  in  terms  of  Human  Progress 

From  another  point  of  view  we  may  realize  the  efficiency  values  of 
force  in  the  aggregate  by  observing  that  human  civilization  as  it  has 
progressed  has  been  marked  by  an  increasing  use  of  various  forces. 
Every  great  man  has  been  full  of  power  of  some  sort,  and  usually 
mere  physical  fire  and  passion  have  been  an  element  or  aspect  of 
this.  So  every  great  race  or  nation  has  had  great  potential  powers 
of  combat  as  well  as  of  constructive  power. 


KINEMATIC  AND   DYNAMIC  221 

Limitations  and  Dangers 

This  part  of  the  discussion  should  not  be  concluded  without  a  con- 
sideration of  the  fact  that  certain  limitations  and  dangers  are  con- 
nected with  the  use  of  force.  Thus  physical  forces  in  general  are 
subject  to  the  limitation  which  has  been  termed  the  dissipation  of 
energy.  This  means  that  forces  when  transformed  tend  to  pass  into 
lower  forms.  Each  particular  form  of  force  also  has  its  own  limita- 
tions. 

Certain  dangers  and  losses  are  also  connected  with  the  use  of 
forces.  Thus  forces  when  used  in  too  large  or  too  small  a  way,  or 
when  otherwise  misdirected,  may  produce  floods,  droughts,  con- 
flagrations, blindness,  or  death. 

As  a  whole,  however,  the  mastery  of  forces  in  connection  with 
matter  and  substance  tend  to  give  a  mechanical  trigger  control  of 
the  universe,  with  a  dialectic  of  resulting  values. 

EFFICIENCY    ANALYSIS    OF    MOTION 

In  classifying  motions  and  more  especially  in  investigating  the 
efficiency  functions  of  motion,  it  has  been  necessary  to  analyze  the 
idea  of  motion  to  a  certain  extent.  Certain  other  remarks  however 
should  be  made  on  this  matter  in  order  to  complete  as  far  as  possible 
the  determination  of  the  fundamental  sources  of  efficiency  contained 
in  this  concept. 

Multiplicative  Nature  of  Motion 

The  motion  of  an  object  implies  certain  diversities  in  the  position 
and  relations  of  the  object,  along  with  a  uniformity  in  the  object 
itself.  This  diversity  and  this  uniformity  are  the  primary  sources  of 
the  group  nature  of  motion,  and  hence  of  most  of  its  efficiencies. 

From  another  point  of  view  the  multiplicative  nature  of  motion 
may  be  realized  by  observing  that  motion  is  a  resultant  of  the  ideas 
of  space  and  time.  We  shall  find  later  that  these  concepts,  from  the 
efficiency  point  of  view,  are  primarily  multiplicative  in  essence. 
Hence  it  follows  that  motion  must  be  essentially  of  the  same  charac- 
ter. The  formulas  which  are  used  to  express  the  laws  of  motion  in 
terms  of  space  and  time  are  multiplicative  in  form  and  hence  illus- 
trate the  principle  under  discussion.  Examples  of  such  formulas 
are  s  =  vt  and  s  =  3^  gt^. 


222  .  SOURCES  OF  EFFICIENCY 

Unique  Element  in  Motion 

In  motion  as  in  other  categories  of  efficiency,  there  is  also  present 
a  unique  and  irreducible  element.  In  other  words,  after  we  have 
analyzed  the  conception  of  motion  as  far  as  we  can  in  terms  of  the 
other  Efficients  and  of  conventional  categories,  something  is  left 
which  is  incapable  of  further  analysis.  This  element  is  the  source  of 
useful  results  in  ways  not  fully  understood,  and  may  at  any  time 
become  the  source  of  still  other  results. 

Definitions 

It  may  be  useful  to  sum  up  the  preceding  discussion  of  the  nature 
of  motion  in  the  form  of  an  approximate  definition. 

Motion  is  a  change  of  position  accompanied  by  a  continuous  and 
manifold  re-multiplicative  grouping  of  an  object  in  relation  to  all 
other  objects  in  time  and  space. 

Each  special  form  of  motion  is  also  capable  of  its  individual 
analysis  and  efficiency  description.    Thus 

Change  is  vague  and  formless  motion;  or  motion  determined 
mainly  by  a  difference  in  an  object  as  viewed  originally  and  after  an 
interval  of  time. 

It  is  sometimes  useful  to  regard  a  motion  as  a  mere  change,  even 
when  the  motion  is  fully  understood.  In  this  case  change  is  the 
prime  group  in  the  system  of  diversities  constituting  the  motion. 

Kinematic  is  a  term  by  which  it  is  convenient  to  denote  the 
abstract  efficiental  essence  of  motion  and  which  it  is  possible  to 
clothe  under  given  circumstances  with  the  more  concrete  categories 
which  give  rise  to  motion  as  conventionally  understood. 

EFFICIENCY  ANALYSIS  OF  FORCE 

The  efficiency  analysis  of  force,  like  that  of  motion,  has  been  made 
in  large  part  in  the  course  of  the  preceding  discussion. 

Multiplicative  Nature  and  Uniqueness  of  Force 

It  may  be  added,  however,  that  the  multiplicative  nature  of  force 
or  energy  may  be  made  more  clear  by  a  detailed  study  of  the  laws 
which  govern  special  forces.  Thus  the  central  forces,  such  as  gravi- 
tation, sound,  magnetism,  and  light,  are  governed  by  what  is  known 
as  the  law  of  inverse  squares.    According  to  this  law,  the  intensity 


KINEMATIC  AND  DYNAMIC  223 

of  each  of  these  forces  varies  inversely  as  the  square  of  the  dis- 
tance from  the  center  where  the  force  originates. 

Force  Hke  motion  also  contains  a  unique  source  of  efficiency 
which  is  constantly  to  be  reckoned  with. 

Definitions 

As  an  approximate  definition  we  have  the  following: 

Force  is  the  aggregate  of  externalities  which  produce  or  prevent 
motion,  directly  or  indirectly. 

Each  specific  form  of  force  also  contains  its  own  specific  sources 
of  efficiency  and  hence  is  capable  of  being  described  in  efficiency 
terms  of  its  own.    Thus 

A  cause  is  a  force,  or  that  which  contains  a  force,  considered  as 
preceding  in  time  the  motion  associated  with  it. 

Potential  as  a  form  of  force  means  latent  force.  The  term  is 
often  used  with  reference  to  the  possible  generation,  throughout  a 
given  area,  of  force  uniform  in  kind  and  degree.  It  is  in  this  sense 
that  lines  or  surfaces  of  equal  potential  are  spoken  of. 

Dynamic  is  a  term  by  which  it  is  convenient  to  denote  the  abstract 
efficiental  essence  of  force  and  which  it  is  possible  to  clothe  under 
given  circumstances  with  the  more  concrete  categories  which  give 
rise  to  force  and  energy  as  conventially  understood. 

METHOD  FOR  MOTIONS 

In  order  to  utilize  motion  to  the  utmost,  it  is  important  usually 
not  to  regard  it  as  mere  vague  or  spasmodic  change,  but  to  realize  it 
as  multiplicative  in  nature. 

Variety  and  Extreme  Forms  of  Motion 

As  with  the  other  Efficients,  this  conception  of  the  category  in 
handmaids  us  in  realizing  the  great  number  of  forms  which  it  can 
assume  by  the  multiplicative  combination  of  different  objects,  paths, 
causes,  and  results.  This  conception  also  helps  us  to  anticipate  the 
extreme  forms  which  motion  may  assume,  and  in  particular  the 
extraordinary  velocities  which  may  characterize  it.  For  evidently 
there  is  no  appreciable  limit  to  speed  which  may  be  generated  by 
even  a  finite  number  of  levers  each  rotating  upon  the  end  of  the 
preceding.     Hence  it  should  occasion  no  surprise  to  find  that  the 


224  SOURCES  OF  EFFICIENCY 

velocity  of  light  is  186,000  miles  per  second,  and  we  are  even  able  to 
deal  with  the  statement  that  the  velocity  at  which  gravitation  acts 
must  be  at  least  7,000,000  times  that  of  light. 

In  all  practical  affairs  it  is  well  constantly  to  realize  that  things 
not  only  hang  together  in  groups,  but  that  they  also  travel  and 
change  in  multiplicative  ways,  as  by  swings  and  rushes,  which 
present  lightning  strokes  of  both  danger  and  opportunity. 

In  cases  of  difficulty  and  limitation  it  is  often  better  to  use  crude 
and  vague  motion  rather  than  no  motion  at  all.  Certain  instances 
where  this  principle  applies  have  been  given  in  the  chapter  on  direc- 
tive action.  A  similar  case  is  that  of  keeping  up  certain  motions  in  a 
merely  formal  way,  while  waiting  for  them  to  pass  into  more  effec- 
tive action. 

Motion  Study  in  Specific  Cases 

The  importance  of  the  specific  study  of  each  individual  kind  of 
motion  has  already  been  pointed  out.  This  applies  to  abstract  or 
ideal  motions  as  well  as  concrete  ones.  Thus  it  is  important  to  note 
that  at  the  present  time  the  use  of  a  new  mechanical  invention 
spreads  rapidly  while  a  new  ethical  or  political  idea  travels  more 
slowly.  Much  of  the  success  of  Napoleon  was  due  to  the  fact  that 
he  knew  the  velocity  with  which  his  armies  could  be  made  to  travel 
and  he  also  knew  the  limits  to  this  velocity. 

In  each  department  of  life  the  detailed  study  of  the  motions 
involved  forms  an  important  source  of  increasing  efficiency.  Men- 
tion has  already  been  made  of  the  increased  efficiency  obtained  in 
bricklaying  by  diminishing  the  number  of  motions  involved  in  the 
laying  of  one  brick.  A  similar  study  of  almost  any  operation  such 
as  husking  an  ear  of  corn  or  harnessing  a  horse  may  produce  similar 
results.  A  like  opportunity  for  increasing  efficiency  is  found  in 
combining  and  arranging  buildings,  rooms  and  parts  of  rooms  so  as 
to  reduce  the  size  and  number  of  motions  of  persons  living  and 
working  in  these. 

The  relative  importance  of  speed  in  different  cases  often  merits 
careful  study.  Thus  great  speed  in  firing  a  battle  ship  is  of  prime 
importance,  while  it  is  of  little  or  no  value  in  calculating  the  date 
of  a  distant  eclipse  of  the  moon. 


KINEMATIC  AND  DYNAMIC 


225 


Auxiliaries  to  Motions 

Mention  should  also  be  made  of  the  importance  of  using  the  best 
possible  auxiliaries  in  connection  with  motions,  as  in  generating  or 
detecting  very  rapid  or  very  slow  motions.  Symbolical  and  mechan- 
ical means  may  also  often  be  made  effective  aids  in  keeping  a 
machine  running  at  its  maximum  speed  efficiency.  Thus  "Mr.  F.  W. 
Taylor  has  succeeded  in  establishing  formulae  sufficiently  trust- 
worthy for  the  production  of  slide  rules  by  which  it  is  possible  to 
determine  in  a  few  minutes  the  best  speed  and  feed  to  use  in  ex- 
ecuting any  given  piece  of  work  in  any  given  lathe  and  with  any 
given  set  of  tools".  With  practice  and  experience  similar  semi- 
mechanical  methods  may  become  more  or  less  instinctive  in  the 
individual  life  with  respect  to  higher  matters  also. 

METHOD   FOR   FORCES 

Similarly,  in  order  to  utilize  forces  to  the  utmost,  it  is  important 
to  regard  them  not  as  mere  vague  thrusts  and  pulls,  but  to  under- 
stand that  they  are  multiplicative  in  their  essential  nature. 

Variety  and  Extreme  Forms  of  Forces 

This  conception  enables  us  to  realize  their  great  number  and 
variety,  their  extreme  forms,  to  grasp  them  in  a  shape  ready  for 
use,  and  to  apply  them  most  effectively.  Thus  the  steam  railroad 
would  have  been  a  practical  fact  much  sooner  if  the  extent  of  the 
friction  between  a  rail  and  the  rim  of  a  wheel  had  been  understood. 
The  efficiency  of  the  steam  engine  comes  largely  from  the  extreme 
facility  with  which  water  vapor  takes  up  large  quantities  of  energy 
and  gives  off  the  same  by  condensation. 

Opposed  Systems  of  Forces 

In  this  connection  it  is  important  to  realize  that  each  case  of 
seeming  rest  or  stability  is  merely  a  case  of  equilibrium  between 
balanced  forces,  and  also  that  these  balanced  forces  are  multiplica- 
tive in  nature.  Thus  in  the  human  body  opposite  sets  of  nerves  hold 
each  other  in  check  and  the  same  is  true  of  muscles.  If  one  set 
is  rendered  inactive,  the  other  set  will  act  often  with  great  energy. 
In  general,  the  universe  is  in  a  state  of  approximate  manifold 
equilibrium  between  opposed  multiplicative  forces.  Any  change  or 
disturbance  in  one  of  two  opposed  sets  of  forces  may  result  in  sudden 


226  SOURCES  OF  EFFICIENCY 

explosions  or  transformations.     In  other  words  all  things  are  in 
a  state  of  triggerish  opportunity  or  danger. 

Study  of  Specific  Forces 

For  this  and  other  reasons  the  importance  of  making  a  specific 
study  of  each  individual  kind  of  force  is  evident.  In  making 
chemical  syntheses,  for  instance,  it  is  found  that  argon  has  too 
small  an  affinity  for  other  substances  to  be  widely  useful,  that 
fluorine  has  too  great  an  affinity,  and  that  the  medium  powers  of 
carbon  in  this  respect  cause  it  to  be  the  most  widely  used  of 
substances.  Similar  special  qualities  are  found  to  characterize  all 
forces. 

Forces  of  High  Order 

Other  things  being  equal  it  is  best  to  use  the  force  which  is  most 
highly  multiplicatively  grouped  in  its  nature  or  properties.  For  it  is 
evident  that  such  a  force  can  be  adapted  most  readily  to  any  given 
end,  such  as  delicacy  or  intensity  of  action.  In  such  forces,  a  less 
costly  form  of  energy  can  most  readily  be  substituted  in  part  for 
a  more  expensive  form. 

The  advantage  of  using  forces  which  govern,  unlock,  or  control 
other  forces  should  constantly  be  kept  in  mind.  It  is  also  best  wher- 
ever possible  to  use  abstract  forces  like  pressure  or  influence  instead 
of  brute,  concrete  forces.  Competition  is  often  an  effective  force 
in  producing  results,  but,  as  a  rule,  it  is  costly  and  of  a  low  order, 
processes  of  cooperation  and  direct  grouping  being  in  themselves 
much  higher. 

In  conclusion  it  is  important  to  keep  in  mind  that  the  highest 
forces  are  those  which  spring  from  the  use  of  the  Efficients  in  some 
form,  and  the  highest  motions  are  those  which  accompany  such 
forces.  For  instance  the  particular  conception  which  a  person  has 
of  the  summum  bonum  governs  the  life  of  that  person,  and  the 
world  life  is  changed  more  profoundly  by  the  views  of  society  in 
this  respect  than  in  any  other  way. 

Hence  the  generation  or  utilization  of  efficiental  force  is  one  of  the 
highest  sources  of  efficiency. 

Summary  of  Chapter 

To  sum  up,  motion  and  increased  speed  are  often  the  sources  of 
efficiency  in  various  ways.     The  same  is  true  of  the  utilization  of 


KINEMATIC  AND  DYNAMIC  227 

forces,  whether  these  be  human  or  external  to  man.  Hence  in  the 
science  of  obtaining  resuUs,  both  motion  and  force  merit  close  study. 
Motions  are  classified  both  with  respect  to  their  forms,  and  also  with 
respect  to  the  objects  which  move.  Similarly  forces  are  classified 
according  to  the  substances  in  which  they  are  contained,  according 
to  the  motions  to  which  they  give  rise,  or  with  respect  to  other 
specific  results  produced  by  them.  Also  some  forces  are  character- 
ized by  a  combination  of  the  above  methods,  examples  being  light, 
heat,  publicity,  and  highest  of  all,  efficiental  forces. 

In  studying  the  efficiency  functions  of  motions,  it  is  convenient, 
first  to  investigate  those  of  pure  motion,  then  those  of  motions 
where  the  force  involved  is  slight,  and  finally  those  of  motions 
which  are  taken  as  representative  of  energy  expended  (as  in  brick- 
laying). The  values  inherent  in  superior  speed  also  merit  particular 
study.  The  fundamentally  useful  property  in  motion  is  that  of 
producing  new  groups,  but  this  property  often  takes  a  multitude  of 
valuable  special  forms,  some  of  them  of  transcendent  value.  Force 
is  useful  as  a  source  of  motion  and  also  in  other  special  ways. 
Hence  human  progress  has  ever  been  marked  by  an  increase  in 
the  amount  and  speed  of  motions,  and  in  the  utilization  of  forces. 

In  order  to  make  the  most  effective  use  of  motion,  its  essentially 
multiplicative  nature  must  be  realized.  Such  a  realization  leads  to 
an  appreciation  of  its  many  varieties  and  of  the  extreme  forms 
which  some  of  these  assume.  Specific  study  of  individual  cases  is 
highly  important.  Every  motion  is  associated  with  some  object  or 
objects,  hence  the  study  of  auxiliaries  in  connection  with  motions  is 
peculiarly  fruitful  in  results.  The  same  remarks  apply  to  the  use 
of  forces.  In  addition  it  should  here  be  noted  that  apparent  rest 
is  due  to  a  balance  of  forces  which,  if  understood,  may  often  be 
happily  manipulated  in  whole  or  in  part.  Stress  should  always  be 
laid  on  efficiental  motions  and  efficiental  forces. 


EXERCISE  13 

1.  Give  an  example  of  each  of  the  principal  kinds  of  motion. 

2.  Also  of  each  of  the  principal  kinds  of  force. 

3.  In  a  given  factory  a  machine  which  is  capable  of  making  200  revolu- 
tions per  minute  is  actually  making  only  50  revolutions  per  minute.  State 
the  speed  efficiency  of  the  machine  as  a  per  cent. 

4.  A  given  factory  contains  four  machines  which  are  being  run  at  M,  Yi,  ^, 


228  SOURCES  OF  EFFICIENCY 

and  H  of  their  possible  speeds  respectively.  If  these  machines  work  in 
parallel  fashion,  find  their  average  speed  efficiency.  If  they  run  tandem, 
find  their  resultant  speed  efficiency. 

5.  Three  hours  of  labor  by  one  man  were  once  required  to  raise  one 
bushel  of  wheat.  Within  the  past  century  this  time  has  been  reduced  to  9 
minutes.  Express  the  degrees  of  relative  efficiency  involved.  What  are 
the  main  sources  of  this  increased  efficiency? 

6.  In  a  given  case  the  cost  of  floating  50,000  tons  of  coal  from  Pittsburgh 
to  New  Orleans  was  $35,000.  To  send  this  coal  by  railroad  would  have  cost 
$150,000.  State  the  degree  of  efficiency  in  the  first  process  as  compared  with 
the  second.     State  the  principle  sources  of  this  efficiency. 

7.  In  moving  a  certain  building  the  wages  of  the  workmen  employed 
amounted  to  $18  per  day.  By  using  a  team  of  horses  at  a  cost  of  $3  per 
day,  the  time  occupied  in  moving  the  building  could  ha\e  been  reduced  from 
six  days  to  two.  How  much  more  efficient  would  the  second  method  have 
been  than  the  first? 

8.  Point  out  the  advantages  with  respect  to  speed  and  power  in  the  use 
of  an  autotruck  as  compared  with  a  dray  drawn  by  horses. 

9.  Give  an  example  in  which  the  superior  speed  of  the  automobile  (as 
compared  with  the  horse  and  wagon)  is  a  means  of  saving  life. 

Give  an  example  of  a  unique  or  transcendent  value 

10.  In  motion      11.  In  superior  speed      12.  In  force      13.  In  superior  force 

14.  Give  an  example  where  a  motion  is  a  useful  symbol  of  a  force. 

15.  Give  an  example  where  a  force  (or  the  material  object  in  which  a  force 
is  stored)  is  a  useful  handle  by  which  to  control  a  motion  or  another  force. 

16.  Some  of  the  air  currents  of  the  upper  atmosphere  travel  with  a  velocity 
of  100  miles  per  hour.  If  these  could  be  utilized  by  an  aeroplane  in  crossing 
the  Atlantic  Ocean,  what  advantages  would  result? 

17.  Give  an  illustration  of  the  power  of  publicity  as  a  social  force. 

18.  Give  an  example  in  which  graceful  motion  is  a  sign  of  efficiency. 

19.  A  laborer  in  husking  one  ear  of  corn  was  observed  to  be  making  eight 
motions.  If  the  same  work  could  have  been  done  with  five  motions,  what 
was  the  degree  of  efficiency  in  his  work? 

20.  Make  up  and  work  a  similar  example  concerning  the  process  of  hitch- 
ing a  horse. 

21.  Harnessing  a  horse  22.  Washing  a  dish 

23.  Name  four  other  processes  of  labor  where  the  work  involved  might 
be  diminished  by  an  analysis  of  the  process  into  constituent  motions, 

24.  Give  an  example  in  which  momentum  (or  inertia)  is  made  a  source  of 
efficiency. 

25.  Point  out  some  of  the  uses  of  friction. 

26.  Show  how  the  dimensions  of  a  force  are  increased  by  the  use  of  the 
hydraulic  press. 

27.  Give  an  illustration  of  the  "power  of  an  idea". 

28.  Give  an  instance  where  it  is  more  advantageous  to  use  abstract  than 
concrete   force. 


KINEMATIC  AND   DYNAMIC 


229 


29.  Give  three  examples  of  the  saving  of  human  labor  by  the  substitution 
for  it  of  the  forces  of  nature. 

30.  Why  is   speed  in   firing  a  gun  on  a  battleship   more  important  than 
speed  in  calculating  an  eclipse  in  an  observatory. 

31.  Give  an  example  where  increased  speed  results  in  loss. 

32.  Give  three  examples  of  the  misuse  of  natural  forces. 

33.  State  the  advantages  to  a  government  of  keeping  the  money  issued 
by  it  in  rapid  circulation.    To  a  merchant,  of  turning  over  his  capital  rapidly. 

34.  State  the  advantages  of  being  able,  in  certain  cases,  to  send  money  by 
telegraph  instead  of  by  mail. 

35.  State  some  of  the  advantages   in  business  conducted  by  competition. 
Also  some  of  the  disadvantages. 

36.  Write  an  account  of  the  increased  utilization  of  motion  as  civilization 
has  progressed. 

37.  Also  of  the  use  of  increasingly  high  velocities. 

38.  Also  of  the  increased  use  of  forces  of  all  kinds. 


CHAPTER  XIII 
RHYTHM 
Illustrations 

After  studying  the  work  of  men  engaged  in  loading  pig  iron  on  a 
car,  F.  W.  Taylor  found  that  in  order  to  load  the  maximum  amount 
in  a  day,  a  workman  must  be  free  from  load  58  per  cent  of  the 
time.  Hence  in  the  Bethlehem  Steel  Works  he  required  men  doing 
this  kind  of  work  to  sit  down  and  rest  at  intervals  so  as  to  bring 
the  part  of  the  time  when  they  were  free  from  load  up  to  the  58 
per  cent.  This  was  an  essential  part  of  the  method  by  which  he 
increased  the  amount  of  pig  iron  loaded  per  day  by  each  man  from 
123^  tons  to  47  tons. 

Similarly  a  great  artist  often  finds  that  he  can  produce  results  of 
the  highest  order  of  excellence  only  by  alternating  long  periods  of 
rest  with  relatively  short  periods  of  intense  exertion. 

Not  only  do  men  consciously  use  the  rhythmic  method  of  work  in 
order  to  gain  added  efficiency,  but  nature  has  also  utilized  the  same 
principle  in  various  ways  in  building  up  efficiency  organisms  like 
plants  and  animals.  An  example  is  the  economy  and  power  in  the 
assimilation  of  food  gained  by  the  rhythm  which  characterizes  the 
digestive  process  in  man  and  the  higher  animals.  The  oscillating 
method  also  is  present  in  many  forms  in  the  inanimate  world  and 
when  rightly  understood  and  utilized  is  a  frequent  source  of  effi- 
ciency. Thus  by  noting  the  tidal  rise  and  fall  of  the  sea,  the 
navigator  is  able  to  pass  over  bars  and  to  enter  harbors  otherwise 
inaccessible. 

General  Statement 

As  a  preliminary  definition  or  description  we  may  say  that  a 
rhythm  is  the  motion  of  an  object  in  opposite  directions  in  alternate 
succession;  or  more  generally  it  is  the  alternate  appearance  and 
disappearance  of  an  object  or  quality.  The  forces  which  produce 
rhythms  are  frequently  complex  and  more  or  less  obscure.  Hence 
it  is  best  usually  to  treat  rhythms  by  means  of  the  motions  which 
characterize  them. 

230 


RHYTHM  231 

CLASSIFICATION 
Objects  Capable  of  Rhythmic  Change 

It  is  an  aid  in  using  rhythms  effectively  to  classify  them  accord- 
ing to  the  objects  which  move  back  and  forth  in  the  vibrations 
involved.  Thus  we  may  have  a  rhythmic  motion  of  a  material 
object,  of  a  force,  or  of  an  idea. 

In  this  connection  it  is  well  to  note  that  every  object  or  entity 
is  subject  to  rhythmic  motion  or  change  of  some  kind,  but  not  of  all 
kinds.  Thus  the  apparently  immobile  stone  by  the  roadside  is 
composed  of  molecules  each  of  which  is  in  a  state  of  constant 
vibration.  These  vibrations  themselves  are  subject  to  other  rhyth- 
mic changes  such  as  those  produced  by  the  daily  and  annual  changes 
in  temperature.  All  sounds  made  in  the  neighborhood  also  cause 
the  stone  to  pulsate  in  other  ways. 

An  investigation  of  the  matter  has  shown  that  a  state  of  mental 
attention  is  not  uniform  and  continuous;  on  the  contrary  it  is  com- 
posed of  distinct  pulses  or  beats.  A  similar  alternation  characterizes 
each  species  of  nervous  and  mental  action,  as  perception,  memory, 
and  emotion. 

Extreme  Cases 

Likewise  what  appears  at  first  sight  to  be  a  uniform  motion  or 
an  increasing  or  decreasing  one,  on  examination  is  found  to  be 
rhythmic  in  some  way,  as  when  it  is  part  of  a  rhythmic  motion  of 
great  amplitude.  Thus  when  a  body  falls  from  an  elevated  point 
toward  the  earth,  it  seems  to  move  in  one  direction  only,  and  with 
a  constantly  increasing  velocity;  but  if  its  motion  were  not  inter- 
rupted, the  falling  body  would  pass  through  the  earth  and  would 
continue  to  vibrate  back  and  forth  past  the  earth's  center.  The  axis 
of  the  earth  is  continually  shifting  its  position  slightly  in  a  complex 
rhythmic  way. 

It  is  also  to  be  carefully  noted  that  the  most  abstract  and  complex 
ideas  and  entities  are  subject  to  rhythmic  change.  Thus  we  have 
rhythms  of  intensity,  availability,  efficiency,  and  of  certain  properties, 
at  least,  of  space  and  time. 

Rhythms  Classified  according  to  Form 

It  is  also  useful  to  classify  rhythms  according  to  their  various 
forms.  Thus  rhythmic  motions  may  be  one,  two,  or  three  dimen- 
sional.    Examples  of  linear  rhythms  are  the  undulations  in  a  rod, 


232  SOURCES  OF  EFFICIENCY 

or  wire,  or  those  made  by  a  point  vibrating  in  a  line  past  another 
fixed  point.  Examples  of  areal  rhythms  are  the  wave  motion  in  a 
sounding  board  or  in  any  surface.  Illustrations  of  solid  rhythms 
are  wave  motions  in  any  fluid  as  in  the  air,  ocean,  or  ether.  The 
lines  in  which  rhythms  of  one  dimension  act  may  be  straight, 
circular,  or  of  any  curved  or  irregular  shape.  An  important  case 
is  that  which  results  from  the  combination  of  a  circular  motion 
with  a  rectilinear  motion,  as  in  the  motion  of  a  point  in  the  tire  of 
a  moving  wagon  wheel. 

Other  Spatial  Forms 

Linear  waves  are  of  two  principal  kinds,  viz. :  ( i )  longitudinal 
waves,  or  alternate  condensations  and  rarefactions  such  as  are  made 
in  the  air  by  a  vibrating  tuning  fork  or  any  sound  wave;  (2)  trans- 
verse waves,  or  vibrations  at  right  angles  to  the  line  of  progress 
of  the  wave,  such  as  are  made  by  a  stretched  vibrating  string,  or 
by  light  in  the  ether. 

Various  wave  motions  may  also  be  grouped  and  classified  accord- 
ing to  the  lengths  of  the  wave  involved,  their  amplitude  (i.e., 
breadth),  their  geometric  form,  or  velocity. 

The  motion  of  a  solid  object  back  and  forth  in  a  line  like  that 
of  a  piston  in  a  cylinder  is  termed  reciprocating  action. 

Spherical  wave  motion  is  one  which  radiates  in  all  directions 
from  a  center  in  a  solid  space,  as  when  sound  travels  in  all  direc- 
tions from  the  object  producing  it. 

In  some  rhythms  the  moving  object  is  not  changed  internally. 
An  example  is  the  earth  as  it  rotates  on  its  axis,  or  revolves  about 
the  sun.  In  other  cases  the  moving  object  does  change  internally. 
Thus  in  wave  motion  in  the  ocean,  as  the  wave  moves  forward,  the 
drops  of  water  composing  the  wave  change  in  their  relative 
position. 

It  is  also  well  to  observe  that  certain  rhythms  may  be  charac- 
terized as  increasing  or  decreasing  in  one  or  more  respects  as  in  the 
length,  amplitude,  or  velocity  of  successive  waves.  An  important 
special  form  under  this  general  class  is  the  infinite  decreasing 
rhythm.  In  some  of  these  the  whole  space  occupied  is  finite  owing 
to  the  fact  that  the  undulations  diminish  in  length;  or  the  time 
occupied  by  the  motion  is  finite  owing  to  the  fact  that  successive 
waves  occupy  less  and  less  time ;  or  a  rhythm  with  an  infinite  num- 
ber of  terms  may  be  finite  in  both  of  these  respects. 


RHYTHM  233 

Numerical  Forms 

Rhythms  may  be  characterized  according  to  the  category  of  num- 
ber in  different  ways.  The  simplest  of  these  is  by  the  number  of  oscil- 
lations involved  in  a  given  instance.  A  much  more  important  stan- 
dard is  the  number  of  objects  which  alternately  become  prominent 
in  a  rhythmic  motion.  Thus  the  vibrating  motion  of  a  single  object 
like  that  of  a  piston  in  a  cylinder  constitutes  a  unitary  rhythm. 
The  dominance  in  turn  of  two  political  parties,  the  alternate  promi- 
nence of  expansion  and  contraction,  or  of  intake  and  output,  are 
cases  of  dual  rhythm.  The  cyclic  changes  of  moisture  through  the 
forms  cloud,  rain,  river,  ocean,  cloud,  constitute  a  case  of  quad- 
ruple or  fourfold  rhythm. 

Similarly  when  two  or  more  simple  or  elemental  rhythms  are 
combined  to  make  a  single  resultant  rhythm,  this  resultant  may  be 
characterized  by  the  number  of  its  components. 

Other  Important  Forms 

With  respect  to  time,  rhythms  may  not  only  be  termed  temporary 
or  permanent,  but  may  also  be  named  according  to  the  periods  of 
time  in  which  a  single  alternation  or  a  cycle  of  alternations  is 
completed.  For  example  we  have  diurnal,  weekly,  monthly,  or 
annual   rhythms. 

With  respect  to  the  category  of  order  (or  direction)  in  many  im- 
portant rhythms  certain  subordinate  parts  may  be  regarded  as 
retrograde  or  back  eddies.  Examples  are  the  method  of  leaping 
ahead  from  one  prominent  point  to  another  in  a  domain  and  return- 
ing from  time  to  time  to  fill  in  details,  or  the  method  of  construc- 
tion and  repair,  of  using  rules  and  exceptions,  or  of  action  and 
reaction. 

In  relation  to  motion,  special  attention  should  be  called  to  what 
may  be  termed  static  rhythms.  Examples  are  a  series  of  land  ridges 
and  depressions,  or  bands  of  alternate  colors  like  the  stripes  of  a 
zebra.  In  some  cases  static  rhythms  are  the  result  of  some  preced- 
ing active  rhythm,  examples  being  the  rings  of  annual  growth  in  a 
tree,  a  set  of  geological  strata,  or  the  series  of  moraines  formed  by 
a  glacier  as  it  alternately  advances  and  retreats.  Also  static  rhythms 
may  give  rise  to  active  rhythms  in  various  ways,  an  example  being 
the  rhythm  in  mental  cognition  as  the  parts  of  a  static  rhythm  are 
viewed  in  succession. 


234  SOURCES  OF  EFFICIENCY 

A  highly  developed  and  very  important  rhythm  is  that  obtained 
by  arranging  the  chemical  elements  according  to  the  periodic  law. 
Similarly  it  is  often  the  source  of  certain  kinds  of  efficiency  to 
arrange  the  elements  of  a  multiplicative  group  system  in  a  cyclic 
linear  order. 

As  to  uniformity  and  diversity  rhythms  may  be  characterized  as 
continuous  or  discontinuous.  Examples  of  the  former  species  are 
the  motion  of  a  wave  in  the  ocean,  or  the  alternate  succession  of  day 
and  night.  Examples  of  the  latter  are  the  periodic  reappearances 
of  17-year  locusts,  or  the  recurrence  of  eclipses.  Also  a  rhythm 
may  be  homogeneous  (or  heterogeneous),  either  as  to  the  material 
which  moves,  or  with  respect  to  the  forms  of  the  oscillations 
involved. 

Grouped  Rhythms 

Evidently  also  rhythms  may  be  grouped  multiplicatively  in  various 
ways.  One  of  these  ways  is  to  combine  a  number  of  rhythms  to 
form  a  resultant,  then  to  make  a  resultant  of  resultants,  and  so  on. 
Or  a  given  rhythm  may  give  rise  to  a  number  of  others,  each  of 
which  in  turn  produces  still  others,  the  process  being  repeated  during 
a  series  of  stages.  For  instance  the  rhythmic  motion  of  the  earth 
about  the  sun  produces  many  derived  rhythms  such  as  the  change 
of  seasons;  each  of  these  secondary  rhythms  gives  rise  to  others 
of  the  third  order  and  so  on.  Similarly  the  alternation  of  day  and 
night  gives  rise  to  a  whole  system  of  derived  rhythms. 

Rhythms  of  High  Order 

Hence  it  follows  that  rhythms  may  be  of  different  orders  in 
various  ways,  or  according  to  different  standards,  the  most  important 
of  these  standards  being  that  of  degrees  of  general  efficiency.  Thus 
a  rhythm  may  be  of  low  order  because  it  belongs  to  a  low  order  in 
a  multiplicative  group  system,  or  because  it  is  feeble  or  slow,  or 
owing  to  the  fact  that  it  is  motion  of  a  material  or  in  a  medium 
of  low  order.  An  instance  of  the  latter  is  the  alternation  in  the 
moods  of  an  insane  person.  On  the  other  hand  illustrations  of 
rhythms  of  a  high  order  are  the  alternate  use  of  the  abstract  and 
concrete  in  education ;  of  individualism  and  collectivism  in  sociology ; 
of  liberalism  and  conservatism  in  politics ;  of  appearance  and  reality, 
or  of  the  relative  and  absolute  in  philosophy.  Other  important  cases 
are  those  where  certain  Efficients,  or  parts  of  Efficients,  are  used 


RHYTHM  235 

in  turn  recurrently.  Thus  it  may  be  the  source  of  great  efficiency 
to  use  a  unit  and  multipHer  in  alternate  succession,  the  product  of 
each  step  being  the  unit  to  which  the  next  multiplier  is  applied. 
Other  important  cases  are  the  alternate  use  of  algebraic  and  graphic 
symbolisms,  whether  in  mathematical  work,  in  art,  or  in  life  in 
general;  of  externality  and  remultiplicative  grouping,  these  taking 
the  form,  for  instance,  of  reading  and  meditation,  or  of  travel  and 
study,  or  of  expansion  and  reorganization  of  any  kind;  of  analysis 
and  synthesis,  as  in  chemistry;  of  idealism  and  realism. 

It  will  be  found  later  that  perhaps  the  most  fundamental  and 
comprehensive  case  of  all  is  the  use,  in  cyclic  succession,  of  phe- 
nomena, categories,  and  the  Efficients. 

Natural  and  Artificial  Rhythms 

It  is  also  important  to  discriminate  between  the  two  leading 
classes  of  rhythms  due  to  the  presence  or  absence  of  the  directive 
principle.    These  are: 

( 1 )  Natural  rhythms  or  those  which  exist  independently  of  man's 
volition,  as  for  instance  the  alternation  of  day  and  night,  or  the 
beating  of  the  human  heart; 

(2)  Artificial  rhythms  or  those  constructed  by  man  more  or  less 
intentionally,  as  the  alternate  use  of  humor  and  pathos  in  a  novel, 
or  the  rhythmic  recurrence  of  the  classical  and  romantic  movements 
in  a  field  of  art. 

It  will  be  found  that  each  of  these  two  classes  has  its  own 
strongly  marked  efficiency  functions.  This  follows  from  the  fact 
that  the  causes  and  sources  of  artificial  rhythms  are  in  large  measure 
under  man's  control,  while  natural  rhythms  must  in  large  measure 
be  dealt  with  as  we  find  them. 

It  is  to  be  noted  in  this  connection  that  certain  rhythms  may  be 
regarded  as  semi-natural  or  semi-artificial.  For  instance  we  have 
rhythms  like  the  swinging  of  a  pendulum  which,  after  being  initiated 
by  man,  continue  to  act  for  a  considerable  period  without  his  aid. 
Also  the  rhythmic  acts  of  one  individual  often  serve  as  objective 
or  natural  rhythms  to  another  person. 

Complex  Rhythms 

It  is  useful  also  to  remember  that  the  above  species  of  rhythms 
may  be  compounded  and  complexed  in  various  ways.     Illustrations 


236  SOURCES  OF  EFFICIENCY 

are  the  network  of  alternations  which  constitute  the  work  of  a  farm 
during  a  year,  or  the  combination  of  rhythms  involved  in  a  musical 
symphony. 

EFFICIENCY    FUNCTIONS   OF    NATURAL    RHYTHMS 

Since  a  rhythm  is  a  form  of  motion  and  also  involves  forces  from 
certain  points  of  view,  it  follows  that  the  efficiency  functions  of 
motions  and  forces  as  presented  in  the  preceding  chapter  hold  also 
for  rhythms  to  a  certain  extent.  However  the  rhythm,  owing  to  its 
individual  characteristics,  is  also  the  source  of  efficiency  in  ways 
peculiar  to  itself. 

In  discussing  the  latter  class  of  uses  it  will  be  an  aid  to  observe 
the  distinction  between  natural  and  artificial  rhythms.  We  shall 
consider  first  the  efficiency  uses  of  natural  rhythms  including  under 
this  head  the  uses  of  artificial  rhythms  when  the  latter  are  viewed 
objectively  or  apart  from  their  originators. 

Illustration  of  Uses  of  a  Natural  Rhythm 

Owing  to  the  somewhat  complex  nature  of  a  rhythm,  the  efficiency 
functions  of  any  specific  rhythm  are  usually  manifold  and  more  or 
less  interwoven.  Thus  a  tide  which  enables  a  navigator  to  carry 
his  ship  over  a  bar  is  a  special  accumulation  of  watef  which  man 
utilizes  by  the  means  of  the  directive  principle.  The  advantage 
in  this  case  may  also  be  immeasurable  in  that  it  might  be  impossible 
to  get  the  ship  over  the  bar  in  any  other  way  when  pursued  by  a  war 
vessel.  Also  if  the  navigator  instead  of  hiring  a  tugboat  uses  the 
tide  to  carry  his  ship  up  a  river,  he  appHes  the  force  principle  of 
efficiency  in  the  shape  of  substitution  of  a  cheap  force  for  a  costly 
one  as  explained  in  the  preceding  chapter.  This  also  constitutes 
another  application  of  the  directive  principle. 

The  interval  of  time  between  successive  tidal  crests  also  constitutes 
an  important  natural  unit,  which  is  not  subject  to  man's  control  and 
is  therefore  not  liable  to  capricious  change.  Owing  to  the  per- 
manency of  the  causes  producing  tides  this  unit  has  an  enormous 
multiplier  giving  rise  to  a  multiplicative  group  system,  which  com- 
prehends all  tides  the  world  over  and  which  is  also  unlimited  in 
time.  The  approximate  uniformity  in  the  depth  of  tides  at  any 
given  place,  together  with  the  slight  rhythm  of  changes  in  this  depth, 
gives  another  cross  multiplicative  group  systematization  of  tides. 


RHYTHM  237 

The  result  is  a  general  system  of  water  changes  which  constitutes  a 
wide  field  for  the  employment  of  the  directive  principle  in  adding 
efficiency  to  the  processes  of  commerce. 

The  units,  uniformities,  and  multiplicative  group  systems  involved 
in  the  daily  rhythm  of  day  and  night  and  the  change  of  seasons  are 
even  less  subject  to  change  and  more  comprehensive  than  those 
connected  with  the  tides,  and  hence  enable  us  to  plan  and  direct  our 
activities  even  more  widely  and  vitally. 

Reuse  in  connection  with  Rhythms 

It  is  to  be  noted  also  that  the  uniformity  which  characterizes  the 
wave  elements  in  a  given  natural  rhythm,  opens  the  way  to  reuse  of 
our  knowledge  of  one  of  these  oscillation  periods  in  connection 
with  all  the  rest  in  the  given  rhythm. 

Also  the  similarity  between  the  general  wave  structure  in  one 
rhythm  with  that  in  other  rhythmic  systems  enables  us  to  apply 
to  the  rest  what  we  learn  concerning  any  one  of  them.  Thus  the 
general  principles  of  wave  motion,  as  for  instance  the  laws  which 
govern  reflection  of  waves  or  their  concentration,  when  once  learned 
can  be  reused  in  mastering  the  properties  of  each  particular  form  of 
such  motion,  as  sound,  heat,  light,  and  electro-magnetic  waves.  This 
method  is  particularly  useful  in  learning  the  action  of  invisible  waves 
by  observing  the  properties  of  those  which  are  visible.  It  was  by 
this  means  that  Herz  arrived  at  the  properties  of  electro-magnetic 
waves  and  opened  the  way  for  wireless  telegraphy. 

Additional  Illustrations 

Another  domain  of  useful  applications  of  natural  rhythms  is 
illustrated  by  the  fact  that  counting  the  number  of  rings  of  annual 
growth  (a  static  rhythm)  on  a  tree  stump  enables  us  to  determine 
the  age  of  a  tree,  and  get  knowledge  which  perhaps  we  could  not 
obtain  in  any  other  way.  Similarly  an  examination  of  a  series  of 
terminal  moraines,  or  of  a  series  of  geological  strata,  gives  us  impor- 
tant knowledge  of  the  past  history  of  the  earth,  perhaps  of  the  present 
position  of  valuable  deposits  as  of  coal  and  iron,  and  thus  enables 
us  to  shape  our  directive  action  more  effectively. 

A  study  of  tidal  action  enabled  George  H.  Darwin  to  determine 
the  past  history  of  the  earth  in  relation  to  the  moon. 

The  arrangement  of  the  chemical  elements  in  the  periodic  system 
made  it  possible  for  Mendeleveff  to  predict  the  existence  of  chemi- 


238  SOURCES  OF  EFFICIENCY 

cal  elements  as  yet  unknown  and  also  to  foretell  certain  of  their 
properties.  It  has  also  aided  men  in  searching  for  and  finding 
these.  Among  the  elements  thus  discovered  were  gallium,  scandium, 
and  germanium.  So  afterward  in  the  year  1894,  when  Ramsay  had 
discovered  argon,  a  gas  distinctively  different  from  the  chemical 
elements  previously  known,  "the  periodic  law  immediately  suggested 
the  existence  of  a  number  of  elements"  allied  to  it.  A  search  was 
made  for  these  and  the  result  was  the  quick  discovery  of  neon, 
krypton,  and  xenon. 

By  the  observation  of  the  long  continued  vibration  of  a  pendulum 
we  obtain  our  most  accurate  determination  of  the  force  of  gravita- 
tion. The  combination  of  two  rhythms  in  such  a  way  that  the  ele- 
vations in  one  correspond  to  the  depressions  in  the  other  often 
forms  the  most  convenient  way  of  obtaining  a  stable  or  uniform 
result.  An  example  is  that  of  obtaining  a  uniform  income  by  invest- 
ing partly  in  the  stock  of  a  company  which  produces  iron,  and 
partly  in  another  company  which  buys  iron  and  uses  it  as  raw 
material. 

A  knowledge  of  the  law  of  action  and  reaction,  on  the  one  hand 
prevents  excessive  optimism  in  times  of  prosperity,  and  on  the 
other  hand  prevents  depression  in  times  of  disaster. 

The  various  efficiency  attributes  of  many  rhythms  as  of  sound, 
light,  color,  flight  of  birds,  dancing,  make  them  sources  of  pleasure 
and  efficiency  beyond  the  possibility  of  complete  analysis  at  present. 

USES    OF    ARTIFICIAL    RHYTHMS 

A  Source  of  Groups  and  New  Power 

The  fundamental  reason  which  has  led  man  to  form  and  use 
rhythms  is  the  fact  that  in  such  rhythms  he  obtains  groups  at  less 
cost  than  in  other  available  ways  and  also  at  times  he  overcomes 
limitations  otherwise  insuperable.  This  principle  was  illustrated  in 
the  opening  paragraphs  of  the  chapter. 

The  element  of  repetition  which  characterizes  a  rhythm  brings 
with  it  an  inevitable  reuse  of  the  groupage  which  is  the  efficiency 
essence  of  each  wave  or  undulation  in  the  rhythm.  The  result  is  not 
only  the  direct  efficiencies  which  characterize  reuse,  but  also  other 
auxiliary  efficiencies  such  as  are  usually  included  under  such  terms 
as  increased  ease  and  mastery.  These  involve  certain  physiological, 
nervous,  and  mental  economies,  externalities,  motion,  force,  and 
various  self-developing  efficiencies. 


RHYTHM 


239 


Illustrations  of  Efficiental  Values 

Particular  forms  of  artificial  rhythmic  actions  are  often  accom- 
panied by  characteristic  groups  of  efficiencies.  In  the  motion  of  a 
piston  in  a  cylinder,  there  is  reuse  of  the  walls  of  the  cylinder.  In 
all  cases  of  reciprocating  action,  some  similar  form  of  reuse  is 
present.  If  a  number  of  persons  alternate  in  the  use  of  an  object, 
as  a  pump,  the  efficiency  of  the  pump  receives  a  large  multiplier,  at 
times  with  the  immeasurable  advantage  of  saving  human  life.  When 
Stonewall  Jackson  made  long  marches  and  won  battles  by  causing 
his  men  to  lie  down  and  rest  at  the  end  of  each  hour  of  marching, 
he  used  repeatedly  the  prime  groups  in  the  physical  powers  of  his 
soldiers.  So  when  a  man  pursues  different  occupations  alternately, 
he  reuses  his  prime  groups  of  body  and  mind  (and  thus  obtains 
a  more  or  less  continuous  use  of  them),  his  more  sensitive  and 
specialized  faculties  being  enabled  to  rest  and  recuperate  in  turn. 

The  back  eddy  method  of  progress,  that  is,  the  method  of  leaping 
ahead  and  then  returning  to  correct  errors  and  to  perfect  details,  has 
the  advantages  which  arise  from  the  use  of  externality  and  from  the 
treatment  of  prime  groups  first  in  a  large  domain  of  material.  To 
take  a  specific  instance,  the  most  efficient  method  of  political 
progress  is  to  proceed  by  certain  definite  steps  and  to  pause  after 
each  step  till  the  reorganization  called  for  by  that  step  has  been 
completed. 

The  alternate  use  of  two  contrasted  objects  or  methods  often 
brings  efficiency  in  the  form  of  a  repeated  use  of  a  reciprocal  unit 
and  multiplier.  This  form  of  efficiency  is  illustrated  in  the  alternate 
use  of  the  concrete  and  abstract  in  education,  or  of  the  object  and 
symbol,  of  4;he  local  and  universal ;  or  in  the  use  of  humor  and 
pathos  in  a  speech  or  in  any  literary  narrative. 

Negative  Values 

Certain  negative  values  often  accompany  the  use  of  artificial 
rhythms.  For  instance  by  the  alternate  conference  of  power  on 
different  political  parties,  important  governmental  evils  are  fre- 
quently removed  or  kept  from  taking  deep  root,  or  are  even  pre- 
vented from  appearing  at  all. 

Transcendent  Fruitages 

The  results  obtained  by  the  use  of  artificial  rhythms  are  often 
transcendent  and  unique.     For  instance  by  the  use  of  the  rhythmic 


240  SOURCES  OF  EFFICIENCY 

method  a  person  is  frequently  able  to  overcome  an  otherwise 
insuperable  difficulty,  or  to  achieve  otherwise  unattainable  results. 
An  illustration  is  the  breaking  down  of  an  obstacle  by  rhythmically 
repeated  blows.  A  more  abstract  case  is  the  solution  of  a  mathe- 
matical or  other  problem  which  would  otherwise  be  insoluble,  by 
the  use  of  successive  like  steps.  A  more  subtle  case  is  that  of  keeping 
an  approximately  straight  track,  as  in  driving  a  bicycle,  by  slight 
deviations  alternately  to  the  right  and  left,  that  is,  by  the  alternate 
use  of  what  may  be  regarded  as  positive  and  negative  externality. 

Complex  Values 

The  above  efficiency  values  may  also  occur  in  various  complex 
forms.  A  comparatively  simple  case  is  that  of  a  preacher  who 
finds  that  he  obtains  better  results  by  preaching  a  highly  developed 
sermon  occasionally  than  by  attempting  to  make  all  of  his  discourses 
masterpieces.  He  thus  not  only  uses  his  own  powers  with  rhythmic 
effectiveness,  but  he  sets  up  certain  useful  rhythms  of  self-activity 
and  interest  in  his  auditors.  A  rotation  of  crops  by  an  agriculturist 
gives  greater  uniformity  in  income,  and  in  the  number  of  laborers 
employed,  prevents  the  accumulation  of  crop  pests,  opens  the  way  to 
economies  in  fertilizers,  and  has  many  other  advantages.  More 
complex  still  are  the  benefits  obtained  from  a  rhythmic  variety  of 
activity  in  the  higher  thought  and  culture  life. 

Limitations  and  Drawbacks 

It  is  to  be  noted  however  that  certain  limitations  and  compensa- 
tions are  often  connected  with  the  use  of  rhythms.  Thus  while 
one  political  party  is  in  power,  the  members  of  the  other  party  are 
frequently  idle  or  not  working  to  their  full  capacity.  Also  a  change 
from  one  party  to  another  may  produce  costly  breaks  and  interrup- 
tions in  efficiency  processes. 

Human  Progress  Marked  by  More  and  Higher  Rhythms 

In  the  aggregate,  however,  in  most  fields,  the  advantages  in  the 
use  of  rhythms  vastly  predominate  over  their  drawbacks.  Hence 
it  is  not  surprising  to  find  that  human  progress  has  been  marked 
by  an  increasing  use  of  both  natural  and  artificial  rhythms,  and  of 
rhythms  which  take  ever  more  comprehensive  and  vitally  effective 
forms.     An  example  of  a  recently  developed  and  highly  effective 


RHYTHM 


241 


form  of  objective  rhythm  is  the  use  of  electro-magnetic  waves  in 
wireless  telegraphy,  and  of  the  propeller  in  aerial  navigation.  In- 
stances of  more  ideal  rhythms  whose  use  has  developed  with  ad- 
vancing civilization,  are  the  alternate  employment  of  liberal  and 
conservative  movements  in  various  lines,  and  the  method  of  leaping 
ahead  and  returning  to  complete  each  step. 

EFFICIENCY   ANALYSIS   OF   RHYTHM 

As  with  the  study  of  the  other  Efficients,  so  here  it  will  be  an 
advantage  to  make  some  investigation  of  the  sources  of  efficiency 
in  rhythms  apart  from  the  partial  presentation  of  the  matter  neces- 
sarily given  in  stating  the  efficiency  functions  of  rhythms. 

Multiplicative  and  Limitation  Elements 

The  group  or  multiplicative  principle  is  present  in  rhythms  not 
only  in  ways  already  indicated  but  also  in  certain  other  ways  as 
with  respect  to  the  principle  of  limitation.  Thus  in  the  vibrations  of 
a  tuning  fork,  as  a  prong  bends  away  from  its  natural  position  the 
resistance  increases  in  a  multiplicative  way  till  a  point  is  reached 
where  the  momentum  of  the  prong  is  overcome  and  the  motion  is 
reversed ;  the  velocity  in  the  opposite  direction  then  increases  in  a 
multiplicative  way  till  it  again  encounters  a  multiplying  resistance, 
and  so  alternately.  In  the  action  of  a  geyser,  in  the  oscillations  in 
the  supply  and  demand  of  an  article  of  trade,  in  successive  waves 
of  insect  pests,  and  their  enemies,  the  same  general  law  is  found 
at  work. 

Externalities  present  in  Rhythms 

The  group  in  some  of  its  developed  efficiental  forms  is  also 
present  in  rhythms.  For  instance  owing  to  the  limitations  inherent 
in  wave  action,  a  space  exists  between  two  successive  waves  or  their 
crests  which  forms  a  natural  externality  to  these  waves  and  also  a 
place  where  other  externalities  may  be  applied.  Another  inherent 
source  of  efficiency  in  a  rhythm  is  the  fact  that  a  rhythm  by  mere 
continued  action  produces  an  externality  homogeneous  with  the 
original  data,  and  one  to  which  the  multiplicative  group  and  order 
of  material  principles  may  be  readily  applied. 

Other  noteworthy  elements  of  efficiency  in  this  respect  are  the 
space  and  time  categories  which  are  combined  in  a  rhythm.     The 


242  SOURCES  OF  EFFICIENCY 

space  category  for  instance  opens  the  way  for  a  multiplicative 
group  treatment  by  introducing  the  idea  of  the  deviation  from  a 
line  (or  standard)  alternately  in  opposite  directions. 

Imperfectly  Understood  Sources  of  Efficiency 

Rhythms  often  contain  certain  dimly  understood  and  perhaps 
transcendent  sources  of  efficiency.  For  instance  it  has  been  found 
that  light  acting  intermittently  on  vegetation  will,  under  some  circum- 
stances, produce  more  rapid  effects  than  light  acting  continuously. 
But  the  reasons  for  such  a  result  are  not  fully  known.  In  the  appli- 
cation of  sewage  to  filter  beds,  intermissions  covering  i8  hours  out 
of  every  24  are  found  to  be  necessary.  By  the  use  of  the  alternating 
electric  current  power  may  be  transmitted  for  long  distances  where 
such  conveyance  would  not  be  practicable  by  the  use  of  the  con- 
tinuous current. 

Different  Aspects 

It  should  be  stated  that  in  classifying  and  using  rhythms  an 
element  of  relativity  is  often  prominent.  Thus  what  is  a  rhythm 
from  one  point  of  view  is  a  mere  collection  of  uniformities  and  dif- 
ferences in  another  aspect.  An  example  is  a  series  of  glacial  ter- 
minal moraines.  Similarly  a  cyclic  repetition  of  a  certain  group  of 
elements  may  often  be  regarded  as  a  linear  multiplicative  group; 
also'a  federal  multiplicative  group  when  made  over  into  a  linear 
form  becomes  a  rhythm.  An  element  of  relativity  is  also  present 
among  different  species  of  rhythm.  For  what  is  one  species  from 
one  standpoint,  may  be  another  species  when  viewed  differently. 

A  preliminary  definition  of  the  rhythm  was  given  on  p.  230.  In 
the  light  of  the  further  analytical  examination  which  has  just  been 
made  a  rhythm  may  be  described  as  a  special  form  of  multiplicative 
group  system  resulting  from  the  operation  of  the  multiplicative  prin- 
ciple in  a  field  of  great  limitation. 

METHODS  OF  APPLICATION 

Multiplicative  Principle  an  Aid  in  Many  Ways 

In  order  to  make  the  most  efficient  possible  use  of  rhythms,  it  is 
important  to  realize  their  many  groupish  or  multiplicative  elements 
and  aspects  and  to  apply  these  aggressively.  Thus  the  multiplica- 
tive principle  enables  us  to  anticipate  the  large  number  of  existent 


RHYTHM  243 

or  possible  rhythms;  to  realize  their  propagative  nature;  to  grasp 
them  in  systems;  and  to  detect,  or  be  prepared  for,  the  appearance 
of  obscure  rhythms  of  extreme  forms,  such  as  a  tidal  wave,  in  any 
time  or  place. 

Rhythms  in  Difficult  Cases 

It  is  important  also  to  realize  that  in  a  situation  of  difficulty  it  is 
often  better  to  use  a  crude  rhythm  rather  than  no  rhythm  or  other 
more  developed  Efficient.  Thus  the  atomic  theory  of  matter  repre- 
sents (or  includes)  certain  useful  ways  of  regarding  the  constitution 
of  matter;  the  ether  hypothesis  includes  other  of  these  useful 
methods.  It  would  be  highly  advantageous  to  combine  these  two 
views  into  a  single  more  fundamental  one.  As  this  cannot  be  done 
at  present,  men  of  science  often  use  the  two  hypotheses  in  alternate 
succession,  and  obtain  many  useful  results  in  this  way. 

Adaptation  to   Special   Situations 

Again  it  is  often  a  matter  of  careful  consideration  to  determine 
what  particular  form  of  rhythm  to  use  in  a  given  case,  or  whether 
indeed  to  use  a  rhythm  or  some  other  Efficient.  For  example  at 
times  it  may  be  best  to  let  a  panic  of  a  fashion  run  its  course  and 
to  wait  for  a  natural  reaction,  instead  of  trying  to  check  the  move- 
ment at  once  or  trying  to  substitute  some  other  process.  In  like 
manner  it  is  important  to  know  when  it  is  best  to  submit  to  a  natural 
rhythm,  as  that  of  day  and  night,  and  when  to  supersede  it  by  an 
artificial  rhythm  consisting  of  periods  of  intense  work  alternating 
with  periods  of  rest  determined  by  special  circumstances.  Thus  the 
rhythm  followed  by  a  person  doing  manual  labor  would  usually 
be  very  different  from  that  employed  by  a  great  artist.  In  this 
connection  as  well  as  with  reference  to  other  considerations  it  is 
important  to  study  the  more  or  less  technical  properties  of  certain 
natural  rhythms,  as  for  instance,  those  of  some  physical  forces,  or 
those  which  characterize  certain  processes  of  physiology,  psychology, 
and  sociology. 

Preference  to  Rhythms  of  High  Order 

Where  a  choice  among  various  rhythms  is  possible,  it  is  of  course 
desirable  to  use  that  one  which  is  highest  in  the  scale  of  efficiency. 
Thus  in  certain  forms  of  the  steam  engine  much  has  been  gained  by 


244  SOURCES  OF  EFFICIENCY 

substituting  a  rotary  for  a  reciprocating  motion.  Similarly  the  rotary 
snow  plow  is  more  efficient  than  one  which  acts  by  direct  thrusts 
and  recessions.  One  of  the  most  profound  and  therefore  useful 
rhythms  is  the  alternation  of  directive  with  laissez  f aire  methods. 

An  important  method  of  elevating  a  rhythm  in  the  scale  of  effi- 
ciency is  to  develop  or  master  it  till  it  becomes  as  automatic  as 
possible,  alike  in  its  main  action,  its  adjustments  in  details,  and  in 
its  ability  to  give  way  to  other  more  efficient  processes. 

Standard  Forms  and  Systems 

With  rhythms  as  with  other  Efficients,  it  is  often  an  aid  to  select 
certain  standard  forms,  and  to  arrange  and  master  these  few  stan- 
dard forms  as  a  multiplicative  group  system.  It  will  be  an  advantage 
wherever  possible  to  give  the  preference  to  these  standard  forms 
and  often  to  utilize  them  by  variant  reuse  instead  of  inventing  alto- 
gether new  forms. 

Externality  often  an  Aid 

Externality  has  important  uses  in  aiding  us  to  discover,  create,  and 
operate  rhythms.  One  rhythm  may  be  a  help  to  others  in  this  respect. 
An  example  is  the  well  known  value  of  song  in  the  operation  of 
both  subjective  and  objective  rhythms. 

It  is  desirable  in  many  cases  to  use  calculus  methods  in  treating 
rhythms;  that  is,  methods  that  are  largely  symbolic  and  mechanical 
and  yet  give  the  results  of  rationality.  An  instance  is  the  analysis  of 
a  rotary  motion  into  two  linear  rhythms  at  right  angles  to  each  other, 
only  one  of  the  two  components  in  many  cases  being  effective.  An- 
other instance  is  the  compounding  of  two  linear  rhythms  to  obtain 
a  circular  rhythm.  A  more  general  instance  is  the  use  of  the  instru- 
ment called  the  harmonic  analyzer. 

In  the  mastery  of  rhythms  many  special  methods  beside  the  direct 
use  of  rhythms  are  available.  Thus  one's  leisure  may  often  be 
profitably  utilized  by  watching  the  rhythmic  motions  involved  in 
weather  changes,  as  in  noting  the  daily  motions  of  storm  centers 
and  anticyclones.  Practice  of  this  sort  aids  in  grasping  the 
equally  large  but  slower  and  more  subtle  rhythmic  alternations  of 
taste  and  thought  in  the  world  life. 


RHYTHM  245 

Ideal  Species 

It  is  an  important  aid  in  obtaining  the  largest  results  from  the  use 
of  rhythms  to  conceive  of  an  ideal  form  of  this  Efficient  and  to  apply 
this  form  under  all  possible  circumstances.  This  ideal  in  its  general 
form  consists  of  the  rhythmic  motion  or  alternate  use  of  the  Effi- 
cients in  efficiental  ways  for  efficiental  ends.  It  is  also  important 
for  each  person  to  study  his  limitations  and  opportunities  and  to  give 
this  ideal  a  special  form  adapted  to  his  circumstances.  This  individ- 
ual species  will  usually  be  found  to  be  some  particular  form  of  the 
processes  of  leaping  ahead  by  use  of  the  best  material  at  hand,  no 
matter  how  fragmentary  and  imperfect  this  may  be,  and  returning 
occasionally ;  in  other  words,  a  making  of  all  of  life  into  a  compre- 
hensive rhythm  of  externality  and  re-multiplicative  grouping. 

Summary  of  Chapter 

By  way  of  summary  for  this  chapter,  we  may  say  that  the  alter- 
nation of  rest  with  work  is  essential  to  the  most  efficient  labor. 
This  is  an  illustration  of  the  many  forms  of  rhythm  each  of  which 
has  its  own  peculiar  uses.  Rhythms  may  be  classified  according  to 
the  objects  in  them  which  change  in  pulsating  ways,  or  according  to 
the  special  forms  of  these  changes.  An  important  distinction  is  that 
between  natural  and  artificial  rhythms.  Special  mention  may  also 
be  made  of  active  and  static  rhythms. 

A  rhythm  means  a  repetition,  and  it  also  often  means  condensations 
in  the  forms  of  waves.  Hence,  in  a  double  way  it  means  the  for- 
mation of  groups,  and  of  group  systems,  accompanied  by  the  useful 
properties  characteristic  of  these  Efficients,  such  as  reuse,  and  often 
the  attainment  of  results  otherwise  inaccesible.  It  is  useful  to  con- 
sider separately  the  valuable  functions  of  natural  and  artificial 
rhythms.  Special  mention  is  to  be  made  of  the  value  of  the  back- 
eddy  method  of  progress;  that  is,  of  the  method  of  leaping  ahead 
and  then  returning  periodically  to  perfect  one's  work.  Human 
progress  has  been  marked  by  increasing  use  of  rhythms,  especially 
of  those  of  the  highest  type. 

The  rhythmic  method  is  particularly  useful  in  difficult  situations. 
Special  study  should  be  given  to  hidden  and  deceptive  forms  of 
rhythm,  and  care  should  be  taken  to  use  the  highest  possible  form 
in  each  particular  case.  The  highest  form  of  all  is  an  efficiental 
rhythm  reduced  to  an  automatic  and  self -developing  form. 


246  SOURCES  OF  EFFICIENCY 

EXERCISE  14 

State  the  class  or  classes  to  which  each  of  the  following  rhythms  belongs : 

1.  Breathing. 

2.  Democracy,  aristocracy,  and  monarchy  when  dominant  in  a  country  in 
cyclic  succession. 

3.  Motion  of  a  bird's  wing. 

4.  Running  around  a  closed  track  repeatedly. 

5.  Daily  change  of   temperature  of  a  typhoid   patient. 

6.  Variations  in  the  length  of  a  solar  day. 

7.  Successive  returns  of  the  same  comet. 

8.  A  sound  which  gradually  dies  away  and  then  disappears. 

9.  The  daily  and  annual  changes  in  the  color  of  prawns. 
ID.  The  so-called  line  of  beauty. 

11.  The  vertebral  column. 

12.  Alternations  of  good  and  bad  times. 

13.  The  alternate  use  of  induction  and  deduction. 

Give  an  example  of  rhythmic  change  of 

14.  Distance  17.  Velocity  20.  Price 

15.  Temperature  18.  Fashion  21.  Value 

16.  Density  19.  Thought 

2,2.  Give  an  example  of  each  of  the  principal  kinds  of  rhythms. 

23.  Give  two  examples  to  show  what  is  meant  by  the  amplitude  of  a 
rhythm. 

24.  State,  as  far  as  you  can,  the  amplitudes  involved  in  Exs.  i-io. 

25.  Mention  the  various  rhythm®  involved  in  the  process  of  walking.  What 
additional  rhythms  are  involved  in  dancing? 

26.  Give  some  of  the  rhythms  which  result  from  the  beating  of  the 
human  heart. 

2.y.  Give  two  examples  of  rhythmic  motions  which  are  so  rapid  as  to  be 
invisible. 

28.  Give  two  examples  of  rhythmic  motions  which  are  difficult  to  perceive 
for  some  other  reason. 

29.  The  average  annual  profits  on  a  certain  farm  when  wheat  alone  was 
raised  were  $4000.  Later  when  rotation  of  crops  was  practiced  the  profits 
averaged  $5500  per  year.    Compute  the  degrees  of  relative  efficiency  involved. 

30.  When  sailors  pull  on  a  rope  they  usually  heave  rhythmically  and  in 
unison.    Why  is  this? 

31.  State  the  uses  or  advantages  connected  with  each  of  the  cases  mentioned 
in  Exs.  1-4. 

Z2.  Give  an  example  of  a  rhythmic  change  in  some  processes  of  trade. 

33.  Mention  a  natural  unit  derived  from  a  rhythmic  motion. 

34.  Give  a  case  where  a  knowledge  of  the  law  of  action  and  reaction  is 
useful. 

35.  Give  two  examples  where  an  equilibrium  or  other  uniformity  is  obtained 
by  the  use  of  an  alternation  across  a  mean. 


RHYTHM 


247 


36.  Give  an  example  of  a  uniformity  obtained  by  the  combination  of  two 
rhythms. 

Z7.  Name  some  book  in  which  humor  and  pathos  are  made  to  alternate 
effectively. 

38.  Also  one  in  which  humor  alternates  with  some  element  of  strength 
other  than  pathos. 

39.  Give  a  case  where  the  use  of  a  rhythmic  action  gives  a  result  otherwise 
unattainable. 

40.  State  the  advantages  of  repeatedly  forgetting  and  relearning  some 
subject.    Also  state  the  disadvantages. 

41.  Show  how  a  rhythm  often  opens  the  way  to  reuse.    Give  illustrations. 

42.  Discuss  the  advantages  and  disadvantages  of  party  government. 

43.  Why  is  it  that  when  clearing  in  the  daytime,  after  a  storm,  the  sky 
is  alternately  overcast  and  clear? 

44.  Mention  a  case  where  it  is  advantageous  to  use  directive  and  laissez 
faire  methods  alternately. 


EXERCISE  15 
Review 

1.  A  yellow  wall  paper  of  a  given  kind  reflects  42  per  cent  of  the  light 
falling  on  it,  and  a  red  wall  paper  16  per  cent.  Express  the  relative  light  effi- 
ciency of  these  two  kinds  of  paper. 

2.  Newton  stated  that  he  had  accomplished  what  he  did  because  he  stood 
on  the  shoulders  of  giants.  What  principles  of  efficiency  are  implied  in  this 
statement? 

3.  In  a  certain  city  the  average  cost  of  delivering  a  ton  of  coal  by  motor 
truck  is  18  cents,  and  by  horse  and  wagon  is  40  cents.  Compute  the  degrees 
of  relative  efficiency  involved.  What  are  the  main  sources  of  superior  effi- 
ciency in  the  first  of  the  two  methods  used? 

4.  What  principles  of  efficiency  are  involved  in  nipping  an  evil  in  the  bud  ? 

5.  Why  was  it  appropriate  for  Homer  to  speak  of  articulate  speech  as 
"winged  words"? 

6.  Name  the  various  uses  which  man  makes  of  the  tides? 
What  is  the  prime  Efficient  involved  here? 

7.  What  efficiency  principles  are  involved  in  the  statement  "The  pen  is 
mightier  than  the  sword"? 

8.  It  costs  $314  to  send  24,000  pounds  of  glass  a  given  distance  as  freight 
at  the  100  pound  rate  and  only  $168  by  the  carload  rate  although  in  the  latter 
case  the  glass  must  be  paid  for  as  if  it  weighed  30,000  pounds.  State  the 
degree  of  efficiency  involved  and  the  source  of  this  efficiency. 

9.  What  Efficient  is  illustrated  in  the  aphorism,  "An  ounce  of  prevention  is 
worth  a  pound  of  cure"? 

10.  A  man  who  was  digging  6  tons  of  iron  ore  by  hand,  later  by  a  steam 
shovel  was  able  to  dig  200  tons  per  day.  State  the  degree  of  labor  efficiency 
involved  and  the  sources  of  the  increased  efficiency. 


248  SOURCES  OF  EFFICIENCY 

11.  A  physician  before  he  used  antitoxin  lost  82  per  cent  of  his  patients 
sick  of  diphtheria.  After  he  used  antitoxin  he  lost  only  8  per  cent.  Compute 
the  degree  of  the  relative  efficiencies  here  involved.  State  the  efficiental 
sources  of  the  increased  efficiency. 

12.  What  Efficients  are  involved  in  the  circulation  of  the  blood  in  the 
human  body?    State  some  of  the  advantages  which  result  from  this  circulation? 

13.  State  the  elements  of  difference  between  a  rotary  motion  and  a  recipro- 
cating action.  Discuss  the  relative  advantages  of  each  of  these  in  snow  plows. 
Also  in  steam  engines. 

14.  What  Efficients  are  implied  in  the  statement  "Thou  hast  ordered  all 
things  in  measure  and  number  and  weight". 

15.  Compute  the  numerical  value  of  8976  X  S79  —  8976  X  577  by  per- 
forming the  multiplications  before  the  substraction  involved.  Also  calculate 
the  value  of  the  expression  by  first  substracting  577  from  579.  Estimate 
the  efficiency  of  the  second  process  as  compared  with  the  first. 

16.  EHscuss  the  ordering  of  objects  or  acts  in  time  as  a  source  of 
efficiency. 

17.  Also  discuss  the  orderly  arrangement  of  objects  in  space  as  a  source 
of  efficiency. 

18.  Discuss  the  combining  of  order  in  time  and  order  in  space  as  a  source 
of  efficiency. 


CHAPTER  XIV 
DIALECTIC 
Illustrations 

In  the  year  1856  a  young  chemist  named  W.  H.  I'erkin  was  at 
work  in  London  on  the  problem  of  the  artificial  synthesis  of  quinine. 
He  did  not  succeed  in  compounding  quinine,  but  in  the  course  of  his 
manipulations  he  accidently  produced  mauve,  the  first  of  the  aniline 
dyes.  This  discovery  not  only  led  to  the  whole  artificial  dye  indus- 
try, but  to  many  other  important  results  of  which  no  one  had  any 
conception  at  the  time.  As  some  one  has  said,  "Who  would  have 
dreamed  that  the  discovery  of  the  first  aniline  dye  by  Perkin  should 
be  an  essential  link  in  the  development  of  modern  bacteriology  and 
therefore  in  the  crusade  against  tuberculosis  and  other  infectious  dis- 
eases?" Similarly  when  Sir  William  Crookes  attempted  to  obtain 
a  more  accurate  determination  of  the  atomic  weight  of  the  chemical 
element  thallium,  he  did  not  have  the  remotest  idea  that  his  work 
would  result  in  the  discovery  of  Roentgen  rays,  or  radium,  and  in  the 
realization  in  some  particulars  of  the  dream  of  the  medieval  alchem- 
ists as  to  the  transmutation  of  metals.  Columbus  failed  to  find  a 
short  route  to  Asia,  but  he  made  the  far  more  important  and  un- 
expected discovery  of  a  new  world  whose  beneficial  influence  on 
the  old  world  is  only  beginning.  Nothing  is  more  blighting  and 
narrowing  than  the  love  of  gold  for  its  own  sake,  yet  the  search 
for  gold  has  been  the  leading  factor  in  the  exploration  of  the  world 
and  in  the  civilization  of  distant  and  barbarous  regions. 

In  business  the  application  of  any  one  kind  of  efficiency  usually 
brings  some  additional  unexpected  useful  results.  Thus  increased 
order  and  system  bring  increased  speed  and  many  other  benefits. 
Rural  free  delivery  of  the  mail  has  compelled  the  improvement  of 
country  roads,  which  in  many  sections  has  led  to  the  consolidation 
of  country  schools  and  to  many  other  wholly  unforeseen  improve- 
ments in  rural  life. 

In  higher  fields  the  greatest  thinkers  tell  us  that  as  a  rule  their 
best  ideas  come  to  them,  not  when  deliberately  and  consciously 
worked  for,  but  in  some  unforeseen,  sudden,  and  isolated  way. 

249 


250  SOURCES  OF  EFFICIENCY 

General  Statement 

The  principle  of  efficiency  illustrated  in  the  above  instances  is  that 
of  the  unexpected  appearance  or  augmentation  of  useful  results, 
owing  to  some  unrealized  development  of  the  group  or  multiplicative 
category.  This  principle  of  efficiency  we  term  dialectic.  This  source 
of  efficiency  has  been  frequently  alluded  to  in  a  more  or  less  casual 
way  in  the  preceding  pages,  but  we  now  propose  to  concentrate  at- 
tention upon  it  for  a  time  and  to  investigate  it  systematically.  In 
one  sense  this  is  a  study  of  by-products,  but  it  is  to  be  remembered 
that  the  by-product  results  here  under  consideration  may  be  much 
more  important  than  the  result  directly  aimed  at,  and  may  develop 
over  long  stretches  of  time. 

Dialectic  in  Different  Fields  of  Material 

Various  dialectic  processes  may  be  grouped  and  classified  accord- 
ing to  the  material  given  at  the  start;  or,  to  express  the  matter  in 
another  way,  according  to  the  fields  in  which  the  different  processes 
operate. 

One  of  these  fields  is  the  world  of  inorganic  matter.  Thus  a 
chemical  element  may  unexpectedly  assume  a  new  allotropic  or 
crystalline  form,  or  even,  as  indicated  above,  be  transmuted  into 
another  element.  Veins  of  gold,  or  deposits  of  other  useful  material, 
are  often  found  in  strange  positions  or  develop  in  unforeseen  ways. 
Inorganic  matter  is  transformed  into  living  matter,  and  physical 
forces  into  biological  and  mental  ones.  Also  forces  seem  at  times 
to  take  on  the  properties  of  matter,  and  vice  versa. 

Living  organisms  evolve  in  surprising  ways,  an  example  being  the 
development  of  the  bird  from  the  reptile.  So  at  any  time,  under  the 
hand  of  the  plant  breeder  a  strikingly  new  and  useful  species  of 
vegetable  life  is  liable  to  appear.  Similarly  a  dialectic  transforma- 
tion may  take  place  in  a  part  of  an  organism,  an  example  being  the 
development  of  the  skin  into  such  diverse  forms  as  the  teeth  and 
the  crystalline  lens  of  the  eye,  or  that  of  hair  into  the  horns  of  cattle. 

In  the  mental  world  we  have  the  various  peculiar  instincts  or 
highly  specialized  psychic  processes  in  animals,  and  in  man  the 
strange  and  unforeseen  ways  in  which  perceptions  or  words  often 
pass  into  actions,  conscious  and  voluntary  acts  into  unconscious  and 
involuntary  ones,  and  the  sudden  and  unexplained  appearance  of 
ideas  often  of  the  first  order  of  importance. 


DIALECTIC  251 

Social  processes  are  so  complex  that  they  are  especially  fitted  as 
a  field  for  the  operation  of  dialectic.  Instances  vary  from  the  capri- 
cious moods  and  actions  of  a  mob  to  the  extraordinary  results  which 
have  sprung  from  the  labors  of  statesmen  like  the  founders  of  the 
American  nation,  of  whom  it  is  said  that  "they  builded  better  than 
they  knew".  Probably  no  one  of  the  American  revolutionary  states- 
men dreamed  that  their  work  would  result  in  the  conversion  of 
China  into  a  republic  within  150  years. 

In  the  ethical  world  the  principle  in  hand  is  illustrated  by  the 
attainment  of  happiness  while  simply  seeking  to  do  one's  duty ;  and 
in  religion,  by  the  extraordinary  phenomena  which  often  attend 
conversion. 

In  the  domain  of  abstract  thought,  we  have  the  development  of  an 
idea  of  space  into  something  that  is  spaceless,  or  of  time  into  the 
timeless,  or,  as  illustrated  by  the  progress  of  modern  scientific 
thought,  of  materialism  into  a  form  of  idealism.  In  like  manner 
idealism  may  give  rise  to  materialism.  The  sudden  development  of 
one  Efficient  into  a  special  form  of  some  other  Efficient  has  been 
frequently  illustrated  in  the  preceding  pages.  The  general  dialectic 
power  of  symbolism  for  instance  has  been  discussed  on  pp.  177-178. 

In  concluding  this  part  of  the  presentation  it  may  be  remarked 
that  almost  every  important  invention  or  idea  has  occurred  to  the 
discoverer  in  some  small  or  special  form  and  has  afterward  not 
only  been  generalized,  but  has  found  many  unanticipated  fields  of 
usefulness.  The  man  who  first  made  a  wheel  could  not  have  dreamed 
of  its  use  as  a  part  of  a  dynamo,  nor  could  Plato  or  Aristotle  have 
anticipated  many  of  the  uses  of  the  terms  idea  and  category  invented 
by  them  respectively. 

Classification  according  to  Form 

In  characterizing  dialectic  processes  according  to  their  forms, 
and  more  particularly  according  to  spatial  and  quantitative  cate- 
gories, many  of  the  terms  used  for  classification  purposes  in  pre- 
ceding chapters  may  be  applied.  Thus  self-developing  processes 
may  be  narrow,  comprehensive,  or  universal;  one,  two,  or  three 
dimensional.  A  dialectic  may  work  from  within  outward,  or  vice 
versa. 

As  to  number,  such  a  process  may  comprise  a  single  event  such  as 
the  discovery  of  the  Fraunhofer  lines,  or  it  may  be  composed  of 
many  events  occurring  simultaneously  or  unfolding  in  succession. 


252  SOURCES  OF  EFFICIENCY 

An  illustration  of  the  latter  species  is  the  application  of  the  spectro- 
scope to  one  unforeseen  field  after  another.  Also  a  dialectic  process 
may  be  dual,  triple,  or  w-fold  in  the  sense  that  it  is  composed  of 
two,  three,  or  n  strands  of  action.  An  important  case  of  two- 
stranded  dialectic  is  a  process  which  consists  of  both  a  movement 
forward  to  new  results,  and  one  backward  to  a  deeper  grasp  of 
sources  and  origins.  For  example,  the  Roentgen  rays  have  both  had 
many  unexpected  useful  applications  in  the  field  of  medicine  and  also, 
by  working  in  the  opposite  direction,  have  thrown  new  light  on  the 
atomic  structure  of  matter.  In  a  similar  manner  a  new  idea  as  to 
business  management  when  introduced  into  an  establishment,  may 
lead  on  the  one  hand  to  a  reorganization  of  the  business  internally, 
and  on  the  other  to  an  extension  of  external  trade. 

An  important  case  of  temporal  dialectic  is  that  in  which  sur- 
prising results  follow  from  being  in  a  given  place  first.  Thus  the 
Puritans  by  arriving  in  New  England  first  dominated  its  civilization 
to  an  extraordinary  degree,  and  like  results  have  followed  from  the 
fact  that  their  descendants  first  settled  many  parts  of  the  western 
United  States. 

A  process  of  reciprocal  dialectic  is  one  in  which  two  elements 
act  and  react  on  each  other,  often  in  rhythmic  fashion,  thus  pro- 
ducing many  unexpected  results.  An  example  is  the  way  in  which 
abstract  science  and  practical  engineering  have  each  developed  the 
other.  A  still  broader  instance  is  the  reciprocal  influence  of  the  new 
and  old  worlds  on  each  other  in  the  development  of  civilization. 

A  somewhat  similar  form  of  dialectic  is  that  which  may  be  termed 
polar.  In  this  the  existence  of  one  strong  form  of  efficiency  tends  to 
bring  into  being  or  to  develop  its  opposite  or  complement.  Thus  in 
business  the  fact  that  one  member  of  a  firm  is  sanguine  and  daring 
may  make  another  member  cautious  and  conservative.  Similarly  a 
materialistic  movement  is  sure  to  beget  some  form  of  idealism,  often 
a  very  extravagant  one.  Polar  dialectics  may  also  be  triple  or  mani- 
fold in  form.  Thus  strong  personalities  often  appear  in  groups  of 
three,  an  example  being  the  group  of  statesmen  consisting  of  Web- 
ster, Clay,  and  Calhoun.  A  larger  group  is  that  composed  of  the 
great  men  prominent  at  the  time  of  the  American  Revolution.  Often 
one  strong  personality  develops  several  others,  each  of  which  is 
strikingly  different  from  the  others  in  some  respect.  Instances 
are  Napoleon  and  his  marshals,  and  Lincoln  and  many  of  the  great 
men  associated  with  him. 


DIALECTIC  253 

An  important  special  case  of  dynamic  dialectic  is  that  which  may- 
be termed  inductive  influence.  An  illustration  is  the  expansive  and 
unifying  effect  upon  one's  ideas  which  often  accompanies  a  walk 
under  the  open  sky  after  a  day's  work  at  the  desk.  More  compre- 
hensive instances  are  the  results  of  living  and  working  near  great 
men,  or  surrounded  by  great  books,  in  particular  those  containing 
efficiental  material  of  high  order  of  any  kind. 

Efficiental  Forms 

It  goes  without  saying  that  dialectic  processes  may  occur  in  groups 
and  also  in  multiplicative  group  systems.  As  an  example  of  the 
latter  we  have  the  extensive  system  of  results  which  followed  from 
the  assumption  of  the  erect  position  by  man  in  his  early  development. 
Among  these,  in  one  direction,  we  have  the  differentiation  between 
hands  and  feet,  and  the  evolution  of  the  opposable  thumb.  In  an- 
other direction  w^e  have  the  grasp  of  a  larger  visual  externality  with 
its  many  efficiental  consequences. 

Processes  of  dialectic  may  be  of  different  orders,  either  because 
they  operate  in  fields  of  material  which  are  essentially  of  different 
orders,  or  because  they  operate  with  different  degrees  of  efficiency. 
An  important  case  of  dialectic  of  higher  order  is  dialectic  of  dialec- 
tic. For  instance  when  one  form  of  evolution  develops  into  a  higher 
form,  as  brute  evolution  into  that  which  is  rational,  we  have  the 
evolution  of  evolution,  or  evolution  of  the  second  order.  Similarly 
we  may  have  dialectic  of  dialectic. 

With  respect  to  externality,  dialectic  processes  may  be  character- 
ized by  the  amount  of  indirectness  in  them.  In  this  connection  we 
also  have  what  may  be  termed  matrix  dialectic.  This  arises  by 
virtue  of  the  fact  that  if  any  process  goes  on  in  a  given  domain,  some 
corresponding  process  must  proceed  outside  of  the  domain.  Thus  in 
tying  up  a  bundle,  or  forming  a  group  of  any  kind,  we  unconsciously 
make  the  rest  of  the  universe  into  a  corresponding  group. 

An  important  instance  of  complex  dialectic  is  the  cumulative  devel- 
opment of  extraordinary  results  which  has  accompanied  the  succes- 
sion of  fundamental  inventions  such  as  articulate  speech,  or  fire. 

EFFICIENCY  FUNCTIONS  OF  DIALECTIC 

Many  of  the  efficiency  properties  and  results  of  dialectic  pro- 
cesses have  been  indicated  in  connection  with  the  preceding  discus- 


254  SOURCES  OF  EFFICIENCY 

sions  and  illustrations.  Others  of  them  have  been  mentioned  more 
or  less  incidentally  in  earlier  chapters.  It  will  be  an  advantage 
however  at  this  point  to  make  a  more  full  and  systematic  statement 
of  the  matter. 

Economies  produced  by  Dialectic 

In  the  first  place,  as  a  dialectic  process  often  gives  an  extra  result 
without  extra  effort  it  is  the  source  of  noteworthy  economies.  For 
instance  when  the  lens  was  invented  and  used  as  a  burning  glass 
and  it  was  afterward  found  that  it  could  be  used  to  remedy  defec- 
tive vision,  the  latter  useful  result  was  obtained  practically  without 
cost.  This  element  of  economy  is  greatly  emphasized  by  the  fact 
that  the  result  obtained  is  frequently  so  different  in  quality  from 
the  anticipated  and  customary  result,  that  the  amount  of  effort  re- 
quired to  hit  upon  it  would  have  been  enormous.  Hence  dialectic 
often  means  force  and  rationality  acting  independently  of  man,  and 
serving  as  substitutes  for  human  work  of  all  orders. 

A  Source  of  Power 

A  dialectic  process  frequently  advances  not  only  without  our  aid, 
but  seemingly  in  spite  of  insuperable  difficulties  or  opposing  forces. 
In  this  and  in  other  ways  it  may  be  regarded  as  producing  direct 
results,  rather  than  as  a  mere  economy. 

The  gain  involved  often  in  effect  constitutes  the  creation  of  a  new 
type  or  object.  An  instance  is  the  evolution  of  the  eye  from  the  skin, 
or  the  bird  from  the  reptile.  Hellriegel  when  studying  the  nutrition 
of  leguminous  plants  in  the  year  1886,  made  the  unexpected  dis- 
covery that  the  roots  of  leguminous  plants  fixate  nitrogen.  The 
result  essentially  amounted  to  the  creation  of  new  processes  of  effi- 
ciency in  agriculture.  In  the  field  of  abstract  work,  as  in  mathemati- 
cal investigations,  this  creative  function  is  even  more  apparent. 

An  important  special  form  of  this  result  is  the  conversion  of  the 
harmful  into  the  useful,  or  of  defeat  into  victory.  The  Colorado 
potato  beetle  at  first  greatly  diminished  the  potato  crop  in  certain 
sections  of  the  country,  but  in  the  end,  by  causing  agriculturists  to 
study  improved  methods  of  potato  culture,  led  to  crops  two  or  three 
times  as  large  as  those  obtained  before  the  appearance  of  the  beetle. 
Similarly  the  San  Jose  scale  has  proved  a  blessing  in  disguise  to 
the  fruit  grower. 


DIALECTIC  255 

Efficiental  Results 

Dialectic  processes  also  produce  efficiency  results  by  giving  rise 
to  new  and  unexpected  diversities  and  uniformities,  and  consequently 
to  the  fruits  of  these  instruments.  As  to  diversities,  the  word 
dialectic  means  literally  a  laying  apart,  that  is,  the  development  of 
new  forms  of  diversity.  A  comprehensive  illustration  is  what  is 
called  the  divergence  of  species  in  the  process  of  evolution.  As 
examples  of  uniformity  results  we  have  the  unexpected  likenesses 
in  efficiental  essence  which  often  appear  in  radically  different  do- 
mains as  in  language,  mathematics,  and  different  branches  of  science. 
Another  kind  of  a  result  is  that  obtained  when  a  few  glimpses  frame 
themselves  together  in  a  continuous  whole.  The  multiplicative  prin- 
ciple often  shows  an  unexpected  power  to  check  and  control  its 
own  exuberance  and  thus  to  produce  uniformity  in  the  guise  of 
relative  unity  and  system.  This  result  often  means  not  only  a 
corrective  of  extravagance  and  error,  but  often  a  production  of  the 
efficiency  values  of  so-called  reality,  or  the  discovery,  or  creation 
out  of  the  relative  and  incidental,  of  an  efficiency  absolute  (that  is, 
of  that  which  has  all  of  the  efficiency  properties  of  the  so-called 
absolute).  A  specific  instance  is  that  in  which  the  observation  and 
practice  of  the  relatively  useful  leads  to  a  recognition  of  an  absolute 
in  morals  (the  categorical  imperative). 

When  a  systematic  (or  multiplicatively  grouped)  arrangement  of 
objects  is  made  in  one  way,  the  result  is  often  found  to  contain  other 
unexpected  cross  systems  of  multiplicative  groups.  Thus  objects 
when  arranged  rectangularly  like  the  squares  in  a  checkerboard  or 
hills  in  a  cornfield  may  be  regarded  as  grouped  systematically  in  a 
vast  number  of  ways  beside  the  original  rectangular  one.  So  a  prob- 
lem in  mathematics  (or  elsewhere)  that  can  be  solved  in  one  way  may 
usually  be  solved  in  many  other  ways.  In  fact  in  any  multiplicatively 
grouped  system  any  element  may  be  taken  as  the  primal  apex,  and  the 
whole  multiplicatively  grouped  with  respect  to  this  apex. 

Also  in  practical  affairs,  where  many  difficulties  are  present,  effec- 
tive system  and  order  are  often  possible  only  because  we  are  able 
to  leave  many  matters  of  secondary  importance  to  take  care  of  them- 
selves. In  this  case  dialectic  adjustment  takes  the  form  primarily  of 
cancellation  and  elimination. 

In  a  process  of  evolution  the  elimination  of  types  between  certain 
standard  forms  may  give  rise  to  a  multiplicative  ordering  of  ma- 


256  SOURCES  OF  EFFICIENCY 

terials.  This  occurs  also  when  the  materials  and  processes  in  a 
business  are  standardized.  An  example  is  the  differentiation  of 
seagoing  vessels  into  certain  well  defined  types.  The  same  develop- 
ment is  evident  in  automobiles  and  railroad  trains. 

A  dialectic  process  often  produces  a  multiplicative  series  in  a  more 
aggressive  way  as  by  the  development  of  a  higher  type  than  any  given 
at  the  start,  and  afterward  of  other  progressively  higher  types.  The 
evolution  of  plant  and  animal  forms  of  life  in  the  past  history  of  the 
world  is  an  example  of  this. 

A  process  of  dialectic  may  give  rise  to  various  other  Efficients 
beside  those  which  have  been  mentioned.  Thus  a  new  and  im- 
portant externality  may  be  obtained  either  in  some  unforeseen  direct 
way,  or  by  a  working  back  to  causes  or  origins,  or  by  a  generation 
of  or  linking  up  with  parallel  procedures.  Similarly  a  dialectic 
process  often  begets  an  important  rhythm,  as  that  of  alternating  steps 
of  analysis  and  synthesis.  A  dialectic  also  may  unexpectedly  pass 
into  or  produce  another  and  often  more  efficient  dialectic.  An  ex- 
treme case  is  the  dialectic  of  dialectic  mentioned  on  p.  253. 

Negative  and  Complex  Values 

Dialectic  also  has  certain  negative  values  or  uses.  Its  corrective 
power  mentioned  above  is  one  of  these.  Others  are  its  power  to 
reveal  weakness  and  limitation.  A  still  more  important  property  in 
this  connection  is  illustrated  by  the  fact  that  certain  evils,  perhaps 
all  evils  in  the  long  run,  are  self -destructive. 

The  complex  values  of  dialectic  assume  many  forms.  One  of 
the  most  important  of  these  is  its  function  of  making  clear  the  best 
ways  in  which  to  use  the  Efficients  in  combination.  These  complexes 
of  its  uses  and  results  also  appear  in  striking  form  in  many  places 
in  human  progress.  It  is  to  be  noted  also  that  these  complex  func- 
tions become  more  prominent  as  the  world  advances.  For  the  more 
the  group  and  multiplicative  principles  are  recognized  and  employed, 
the  more  numerous  and  important  will  be  their  unexpected  mani- 
festations and  fruitages. 

Limitations  and  Drawbacks 

It  is  not  to  be  overlooked  that  dialectic  as  an  instrument  of  effi- 
ciency has  certain  drawbacks  and  limitations. 

Some  of  these  are  inherent  in  its  nature.    Thus  it  is  often  slow 


DIALECTIC  257 

and  acts  in  a  blind  and  costly  way.     Usually  it  is  not  flexible  and 
readily  manageable. 

Again  it  frequently  acts  in  a  destructive  instead  of  constructive 
way.  Thus  a  mistake  or  evil  may  multiply  itself  in  an  unexpected 
manner.  A  scratch  may  produce  death.  Even  that  which  is  good 
in  itself,  owing  to  the  presence  of  other  unsuspected  evils  or  limi- 
tations, may  become  a  source  of  harm.  An  example  is  the  injurious 
results  which  have  followed  from  the  introduction  of  rabbits 
into  Australia.  In  business  and  in  life  in  general,  one  must  be 
constantly  on  the  lookout  for  some  unexpected  accident  or  other 
extraordinary  unfavorable  development,  and  if  possible  have  abun- 
dant means  ready  to  meet  such  emergencies. 

EFFICIENCY  ANALYSIS 
Result  of  the  Multiplicative  Principle 

The  primary  cause  which  gives  rise  to  dialectic  as  an  efficiency 
instrument  is  the  unrealized  prodigality  of  results  in  a  multiplicative 
process.  For  example  2^^^  when  multiplied  out  gives  a  number  so 
large  that  counting  at  the  rate  of  100  per  minute  it  would  take  a 
billion  billion  years  to  count  all  the  units  included  in  the  number. 
In  other  words  the  ramifications  of  the  multiplicative  principle  are 
so  broad  and  comprehensive,  that  frequently  no  one  at  the  outset  of  a 
given  application  of  it  can  grasp  them  all  in  detail. 

This  holds  often  even  with  respect  to  a  single  group.  The  extent 
of  the  group  may  be  so  great  as  to  be  only  in  part  realized,  or  the 
developments  of  other  groups  may  mask  or  hide  the  given  group 
in  part  or  entirely,  for  the  time  being.  An  understanding  of  this 
makes  it  clear  why  a  mere  change  of  position  or  of  point  of  view 
often  produces  such  vast  consequences.  These  unrealized  cluster- 
ings and  hangings  together  of  objects,  may  take  special  group 
forms,  as  those  of  imperfectly  grasped  reuse,  units  and  multipliers, 
externality,  etc.  Thus  George  Westinghouse  when  he  invented 
high  pressure  gas  mains  did  not  realize  that  he  had  discovered 
a  process  whose  essence  he  could  use  later  in  transmitting  electricity 
at  high  pressure.  When  a  certain  differential  equation  was  first 
formed  and  solved,  its  author  did  not  anticipate  that  this  solution 
when  applied  to  the  Atlantic  cable  would  result  in  making  this 
cable  a  practical  success.  Owing  to  the  common  efficiental  essence 
in  a  number  of  seemingly  diflferent  acts,  or  in  a  number  of  depart- 
ments, in  learning  to  do  one  thing  we  often  unconsciously  learn  to 


258  SOURCES  OF  EFFICIENCY 

do  a  vast  number  of  other  things.  The  often  unnoticed  uniformity  in 
the  size  of  algebraic  symbols  is  the  source  of  many  of  their  dialec- 
tic properties  .  The  outcome  of  a  dialectic  process  often  takes  a 
rhythmic  and  in  part  paradoxical  form.  When  typesetting  machin- 
ery was  invented  it  at  first  diminished  the  number  of  compositors 
employed,  but  later  had  the  unexpected  result  of  increasing  this 
number.  If  the  matter  had  been  viewed  in  a  broad  way  this  result 
might  have  been  anticipated  at  the  start.  An  economical  use  of  one's 
powers  often  results  in  dialectic  results  owing  to  the  fact  that  part  of 
a  person's  energy  is  left  free  to  be  employed  in  any  high  field  which 
he  may  choose. 

If  the  manifoldnesses  involved  in  a  single  group  are  difficult  to 
realize,  much  more  difficult  is  it  to  grasp  all  the  meanings  and  uses 
involved  in  a  whole  system  of  groups.  This  was  illustrated  for 
rectangular  arrays  of  elements  on  p.  255.  And  vastly  more  difficult 
will  it  be  to  comprehend  all  the  ramifications  and  intersections  of 
several  systems  of  groups.  Thus  modern  bacteriology  is  due  to  a 
number  of  factors  each  unfolding  in  multiplicative  style.  The  first 
is  Pasteur's  study  of  ferments,  including  a  use  of  diversity  in 
various  forms,  of  various  externalities,  of  directive,  and  other  Effi- 
cients. The  second  was  Perkin's  discovery  of  aniline  dyes;  the  third 
was  the  improvements  in  the  microscope  itself,  due  to  a  number  of 
causes  such  as  the  invention  of  Jena  glass.  Other  more  general 
factors  might  be  specified. 

Element  of  Spontaneous  Force 

Another  primal  element  of  efficiency  in  dialectic  is  a  certain 
apparently  spontaneous  force  or  energy  which  characterizes  such 
processes.  This  force  may  be  more  or  less  concrete  like  many  of 
those  involved  in  ordinary  physical  growth,  or  it  may  be  abstract 
and  efficiental  in  nature.  As  an  example  of  the  latter  force  or 
energy,  we  have  the  fact  often  noted  that  when  a  group  has  been 
once  formed  it  tends  to  increase  in  size,  the  reason  being  that  laws 
of  increased  efficiency  in  a  measure  compel  such  a  result.  The  force 
in  a  dialectic  process  may  also  be  due  in  part  to  the  action  of 
unconscious  subjective  powers  in  a  person  or  persons  associated 
with  the  process.  These  various  forces  may  also  have  a  highly 
multiplicative  structure  which  also  is  imperfectly  realized.  Hence, 
for  instance,  the  surprising  results  which  often  follow  from  merely 
making  a  start  in  any  enterprise,  as  for  example,  the  spontaneous 


DIALECTIC  259 

flow  of  words  and  ideas  which  follows  the  mere  taking  of  one's  pen 
in  hand.  Some  kind  of  difficulty  or  obstacle  often  stimulates  this 
subjective  multiplicative  apparatus  into  action.  This  perhaps  is 
the  cause  of  the  fact  that  a  haze  or  gauze  when  thrown  on  a  beauti- 
ful object,  often  increases  the  charm  of  the  object.  In  its  most 
general  and  aggressive  form  this  subjective  factor  in  dialectic  is  a 
generalization  of  Kant's  doctrine  of  subjective  categories. 

The  above  various  factors  are  often  combined  in  a  process  of  dia- 
lectic. Thus  when  a  business  like  that,  for  instance,  of  the  manu- 
facture of  glass  is  once  established  in  a  given  place,  it  will  often 
grow  surprisingly,  even  though  the  place  has  no  special  adaptation  to 
the  business. 

In  modern  life  the  number  of  multiplicative  processes  simulta- 
neously at  work  in  the  social,  educational,  and  business  worlds,  and 
in  private  individual  lives,  is  so  great  that  surprising  results  are 
constantly  appearing. 

Element  of  Limitation 

In  order  fully  to  account  for  processes  of  dialectic,  an  element 
of  limitation  must  be'taken  into  the  account.  This  element  appears  in 
two  principal  forms,  viz. :  our  inability  to  grasp  all  the  ramifica- 
tions of  a  multiplicative  process  and  in  the  obstructions  or  difficulties 
which  make  a  process  more  or  less  necessary,  and  hold  it  in  check 
throughout  its  progress. 

Unique  Element 

In  dialectic,  as  in  each  other  Efficient,  there  is  also  present  a 
unique  and  characteristic  source  of  power.  After  we  have  carried 
as  far  as  we  can  our  analysis  of  the  instrument  in  hand,  an  irredu- 
cible something  is  left  over. 

It  may  be  well  also  to  call  attention  to  the  respects  in  which 
dialectic  differs  from  efficiency  processes  in  general.  These  are  the 
element  of  unexpectedness  in  its  results,  the  obscurity  of  many  of 
its  elements,  the  native  force  and  energy  which  carry  it  forward, 
and  its  rationality  apart  from  human  interference. 

Above  all  it  is  to  be  borne  in  mind  that  dialectic  is  not  mere 
vague  haphazard  change  in  which  some  useful  spot  is  occasionally 
observed,  but  that  it  is  a  multiplicative  process  imperfectly  appre- 
hended and  hence,  by  careful  study  and  some  management,  capable 
of  producing  increasingly  important  results. 


26o  SOURCES  OF  EFFICIENCY 

Definitions 

As  an  approximate  definition  we  may  take  the  following : 

Dialectic  is  an  efficiency  process  in  which  results  come  of  them- 
selves, in  whole  or  part,  and  are  therefore  altogether,  or  in  some 
respect,  unanticipated. 

It  may  be  well  also  to  define  a  few  similar  terms. 

Development  is  a  vague  and  general  species  of  dialectic.  It  may 
produce  results  which  are  either  higher  or  lower  than  the  data,  or 
which  are  mixed  in  character. 

Progress  means  a  somewhat  more  definite  series  of  changes  than 
development  and  leads  to  plainly  useful  results. 

Evolution  is  a  dialectic  process  in  which  limitation  is  prominent, 
the  steps  are  small,  the  process  slow,  but  the  change  is  toward 
what  is  higher. 

METHOD  OF  APPLICATION 

Multiplicative  Principle  an  Aid  in  Various  Ways 

A  realization  of  the  multiplicative  nature  of  dialectic  is  an  aid 
in  many  ways  toward  the  full  utilization  of  this  instrument  of 
efficiency.  For  instance  it  facilitates  a  grasp  of  the  great  number  of 
results  which  may  be  obtained  from  this  source,  the  extreme  forms 
of  some  of  them,  and  the  explosive  suddenness  with  which  results 
may  appear. 

It  also  facilitates  the  arranging  different  forms  of  dialectic  in  an 
order  of  materials  scale  and  thus  aids  in  applying  to  a  given  domain 
of  material  that  form  of  dialectic  which  is  best  fitted  to  this  field. 
Thus  in  certain  difficult  cases  only  the  crudest  form  of  dialectic  can 
be  used.  Instances  are  the  use  of  mere  motion,  as  in  shaking  a 
fluid  or  agitating  a  situation,  and  waiting  to  see  what  results  will 
follow ;  or  the  use  of  the  mere  juxtaposition  or  separation  of  the  two 
objects.  An  important  general  case  is  the  Baconian  method  of  group- 
ing facts  according  to  their  likenesses  or  differences,  and  waiting  for 
general  laws  to  appear  among  the  spatial  groups  thus  formed.  Bacon 
himself  would  be  astounded  at  the  results  which  have  already  been 
obtained  by  his  method.  Dialectic  by  induction  (see  p.  253)  may 
also  be  useful  as  an  initial  method  in  a  difficult  case. 

Uses  of  Crude  Dialectic 

A  less  crude  form  of  dialectic  is  that  of  making  a  start  toward  a 
given   end,   and   using  light   and   power   as   these   appear.      In   its 


DIALECTIC  261 

more  advanced  form  this  process  consists  in  the  rhythmic  use  of  suc- 
cessive externalities  and  re-multiplicative  groupings,  and  the  utili- 
zation of  the  dialectic  results  which  appear  at  each  stage  of  the 
process. 

In  a  difficult  case  it  is  often  well  to  avail  oneself  of  dialectic 
in  the  double  form  often  called  compromise.  A  compromise  in  effect 
frequently  consists  in  allowing  two  or  more  methods  or  processes  to 
develop  till  one  of  them  becomes  clearly  more  efficient  than  the 
other,  or  some  new  method  more  effective  than  either  appears  on 
the  scene. 

Preference  to  Dialectic  of  High  Order 

The  aim  should  be  in  all  cases  to  make  the  dialectic  used  of  as 
high  an  order  as  possible.  Beside  the  dialectic  processes  of  high 
order  of  efficiency  described  on  p.  253,  special  mention  may  here  be 
made  of  that  process  which  consists  essentially  of  perfecting  the 
prime  groups  of  a  given  domain  or  piece  of  work  to  the  utmost,  and 
leaving  the  rest  of  the  process  largely  to  dialectic  development. 
Another  important  species  is  that  which  emphasizes  the  self  correc- 
tive power  in  multiplicative  processes,  and  thus  makes  it  possible  to 
use  aggressive  methods  in  an  imperfectly  known  field.  Special 
emphasis  should  also  be  laid  on  the  ideal  form  described  on  p.  263. 

Standard  Varieties 

With  dialectic  as  with  the  other  Efficients  it  is  important  when  a 
good  unit  form  has  been  found  to  reuse  that  species  to  the  utmost ; 
or,  to  express  the  matter  in  another  form,  to  give  it  as  large  a 
multiplier  as  possible.  An  illustration  is  the  generalization  of  a 
principle  or  method  by  using  the  dialectic  habit  which  leads  us, 
when  we  have  thought  of  the  numbers  one,  two,  three,  also  to  think 
of  any  number  however  large.  Thus  having  observed  that  anti- 
toxin aids  in  the  cure  of  diphtheria  in  a  few  cases,  the  query  arises 
in  our  mind  whether  it  may  not  be  an  aid  in  all  cases.  This  process 
may  often  be  repeated  to  advantage  in  many  different  fields.  A 
similar  use  may  be  made  of  the  letters  of  the  alphabet  taken  in 
order.  Other  standard  cases  are  the  dialectic  which  come  from  the 
use  of  the  comparative  method  (that  is,  manifold  homogeneous 
externalities)  in  scientific  and  historical  investigations,  or  from  the 
method  of  transformations.    An  extreme  form  of  the  latter  is  that 


262  SOURCES  OF  EFFICIENCY 

of  expressing  any  given  process  in  terms  of  any  given  Efficient,  or, 
expressing  each  Efficient  in  terms  of  the  other.  Having  mastered 
a  few  standard  forms  of  dialectic  it  is  often  an  advantage  to  arrange 
these  as  a  multiplicative  group  system,  as  an  aid  in  using  them 
either  directly  or  by  variant  reuse. 

Relation  to  Other  Efficients 

Added  efficiency  in  the  utilization  of  dialectic  is  often  obtained  by 
studying  the  relations  of  this  agent  to  each  of  the  Efficients.  For 
instance,  it  has  been  observed  that,  as  the  result  of  dialectic,  a  sud- 
den, explosive  disaster  or  opportunity  is  liable  to  occur  at  any  time. 
Hence  the  importance  of  having  on  hand  some  margin,  reserve,  or 
other  externality  is  apparent.  This  externality  should,  if  possible, 
be  of  such  a  kind  that  it  can  be  utilized  in  other  ways  in  case  the 
accident  allowed  for  does  not  occur.  Thus  it  is  well  to  allow  a 
margin  of  time  in  starting  for  a  train,  and,  in  case  no  unforeseen 
contingency  arises  to  consume  this  margin,  to  spend  the  unoccupied 
time  in  reading.  The  same  principle  applies  to  vastly  wider  and 
higher  fields. 

It  is  especially  important  to  know  where  to  use  directive  and  dia- 
lectic in  relation  to  each  other.  Often,  as  already  indicated,  effi- 
ciency is  obtained  by  using  the  two  instruments  in  alternative 
succession,  or  in  some  other  mottled  way.  Frequently  the  directive 
part  of  an  operation  should  consist  of  the  mere  selection  and  launch- 
ing of  the  proper  dialectic  process. 

In  general,  after  any  efficiental  process  has  been  worked  out 
consciously,  an  added  element  of  power  and  efficiency  can  often 
be  conferred  upon  it  by  developing  it  till  it  acts  in  more  or  less 
dialectic  fashion. 

Special  conventional  forms  of  dialectic,  such  as  growth,  evolu- 
tion, and  development,  are  utilized  most  effectively  when  viewed 
explicitly  as  species  of  dialectic,  that  is,  as  essentially  multiplica- 
tive in  nature. 

Ideal  Species 

From  the  point  of  view  under  consideration  in  this  book  the  ideal 
form  of  dialectic  is  that  which  proceeds  from  efficiental  material,  and 
acts  in  efficiental  ways  to  produce  efficiental  results.  To  look  at  the 
matter  in  more  detail,  we  can  conceive  of  the  Efficients  as  so  per- 


DIALECTIC  .  263 

fected  that  they  will  of  themselves  attack  every  point  of  need 
or  opportunity  with  manifold  power,  speed,  and  adaptation.  In  other 
words  the  process  would  possess  the  highest  mechanistic  and  ration- 
alistic properties  in  combination.  The  fact  that  processes  of  dia- 
lectic in  actual  operation  fall  so  far  short  of  this  ideal,  shows  that 
some  principle  of  a  limitation  is  at  work,  and  it  is  this  principle 
which  we  shall  next  investigate. 

Recapitulation  of  Chapter 

As  a  summary  of  this  chapter  we  may  say  that  when  working  for 
a  given  end,  a  person  is  often  surprised  by  the  appearance  of  some 
valuable  result  which  had  not  been  anticipated.  Often  this  unfore- 
seen fruitage  exceeds  in  value  the  end  consciously  aimed  at.  The 
principle  of  efficiency  here  involved  is  termed  dialectic.  It  acts  in 
all  fields,  from  those  which  are  material  and  inorganic,  to  those 
which  are  most  abstract  and  ideal.  The  species  of  dialectic  may  also 
be  usefully  classified  according  to  the  various  forms  in  which  they 
occur.  Special  mention  may  be  made  of  the  kinds  termed  recipro- 
cal, polar,  and  inductive. 

Since  the  process  of  dialectic  acts  in  hidden,  unforseen  ways,  the 
results  obtained  from  it  may  often  be  regarded  as  obtained  abso- 
lutely without  cost.  Hence  dialectic  is  a  peculiarly  effective  source 
of  economy  and  new  power.  Frequently  a  process  of  this  kind 
gives  rise  to  one  or  more  of  the  Efficients  with  their  corresponding 
fruitages.  Dialectic  also  in  special  ways  and  to  a  peculiar  degree 
supplies  an  element  of  charm  and  even  of  romance  to  kinds  of 
work  which  might  otherwise  be  limited  in  interest. 

Since  dialectic  is  primarily  due  to  the  multiplicative  principle 
acting  in  one  or  more  unobserved  ways,  in  order  to  be  able  to 
utilize  this  source  of  efficiency  to  the  utmost,  a  person  must  obtain 
some  grasp  of  the  great  profusion  of  results  which  may  arise  from 
the  action  of  the  multiplicative  principle  in  even  one  form,  and 
hence  of  the  vastly  greater  number  of  results  arising  when  two  or 
more  species  of  it  act  in  combination.  This  will  make  plain  that 
no  one  can  anticipate  all  the  forms  which  dialectic  may  assume.  In 
cases  of  great  difficulty,  after  initiating  elementary  efficiency  pro- 
cesses, much  may  be  left  to  dialectic  self -development  aided  by. 
occasional  efficiental  regulation.  In  general,  also,  it  is  highly  im- 
portant to  study  and  utilize  the  relations  of  dialectic  to  the  other 
Efficients. 


264  SOURCES  OF  EFFICIENCY 

EXERCISE  16 

1.  Give  an  example  of  each  of  the  principal  forms  of  dialectic. 

2.  Reinforced  concrete  was  first  invented  in  modern  times  by  a  French 
gardener  in  making  reservoirs  for  water.    Give  some  unexpected  results. 

3.  Name  some  of  the  by-products  now  obtained  in  the  manufacture  of 
steel. 

4.  In  the  refinement  of  oil. 

5.  State  the  dialectic  of  uses  of  a  telephone  directory. 

Give  an  example  where  the  result  of  a  dialectic  process  is 

6.  A  multiplicative  group  system. 

7.  A  uniformity.  8.  A  diversity  9.  An  externality 

10.  Name  some  of  the  unexpected  evil  results  which  have  followed  the 
invention  of  printing. 

11.  Give  an  instance  of  your  own  of  loss  produced  by  dialectic. 

12.  Give  an  example  of  a  dialectic  process  resulting  from  a  positional 
relation. 

13.  Name  some  of  the  dialectic  results  which  have  followed  from  Napoleon's 
wars  upon  Germany. 

14.  State  some  of  the  unforeseen  advantages  which  may  come  to  a 
business  man  from  keeping  a  considerable  reserve  of  cash. 

15.  To  any  person  from  having  a  reserve  of  physical  vigor. 

16.  Give  an  example  where  the  use  of  system  or  organization  has  brought 
unexpected  efficiency  results. 

17.  As  a  blacksmith  hammers  he  often  sings  and  as  he  sings  he  hammers 
with  greater  energy  and  precision.     Discuss  the  dialectic  involved. 

18.  Why  is  it  that  if  one  member  of  a  family  expends  his  energies  largely 
in  processes  of  thought,  some  other  member  is  likely  to  become  a  person  of 
action. 

19.  Discuss  the  dialectic  results  of  a  notebook  kept  by  a  business  man. 

20.  By  a  literary  man. 

21.  Methods  of  wrong  doing  are  often  self  destructive  in  unexpected  ways. 
Give  an  example  of  this  species  of  negative  dialectic. 

22.  If  a  primitive  man  in  building  a  camp  fire  happened  to  place  a  lump  of 
iron  ore  among  the  stones  about  the  fire  and  thus  discovered  the  metal  iron, 
what  principle  of  efficiency  was  involved? 

23.  Discuss  the  rhythmic  dialectic  relations  of  fire  and  iron  in  their  histori- 
cal development. 

24.  Mere  formal  imitation  of  a  process  often  ends  in  an  intelligent  grasp  of 
the  same.    What  Efficient  is  here  involved? 

25.  Give  an  instance  where  it  is  advantageous  to  use  the  directive  and 
dialectic  methods  in  alternate  succession. 

26.  Give  an  example  of  a  difficult  case  where  only  cnide  dialectic  can  be 
employed. 


CHAPTER  XV 

LIMITATION 
Illustrations 

In  the  eighteenth  century  the  invention  in  England  of  machine 
and  factory  methods  of  weaving  cloth  and  manufacturing  other 
articles  caused  a  considerable  part  of  the  rural  population  to  move 
to  the  towns  and  cities  for  the  sake  of  the  higher  wages  there 
obtainable.  The  result  was  a  scarcity  of  agricultural  laborers. 
This  compelled  the  landowners  to  study  means  of  meeting  the  de- 
ficiency, the  outcome  being  certain  improved  methods  of  agriculture, 
the  most  important  of  which,  perhaps  was  the  systematic  use  of 
the  horse  with  adapted  implements.  In  this  way  not  only  was  the 
deficiency  in  hand  labor  made  up  but  additional  results  were  ob- 
tained which  have  ever  since  given  England  the  leadership  in  agri- 
cultural efficiency. 

No  living  person  can  run  lOO  yards  in  less  than  9^  seconds,  and 
probably  this  record  will  never  be  excelled  by  more  than  a  fraction 
of  a  second.  A  knowledge  of  facts  like  this  may  be  made  the  source 
of  important  efficiencies.  Thus  in  the  loading  and  firing  of  a  12-inch 
gun  in  the  United  States  navy,  by  careful  study  it  has  been  found 
that  the  shortest  times  in  which  the  various  operations  involved 
can  be  performed  are  in  seconds,  as  follows:  ^,  3^,  4>^,  ^,  2^. 
By  organizing  the  work  of  gun  practice  in  accordance  with  these 
facts  the  firing  efficiency  of  the  fleet  has  been  increased  several  hun- 
dred per  cent.  The  heat  obtained  by  burning  a  pound  of  coal  is  lim- 
ited to  a  certain  amount.  In  whatever  ways  physical  energy  may  be 
transformed,  it  can  never  be  increased  or  decreased.  These  facts 
have  enabled  engineers  to  determine  the  amount  of  waste  energies  in 
steam  engines  and,  by  diminishing  this  waste,  to  increase  the  effi- 
ciency of  such  engines  threefold. 

General  Statement 

The  above  instances  illustrate  the  fact  that  the  efficiency  of  pro- 
cesses is  subject  to  various  limitations.  Some  of  these  limitations 
are  insuperable  in  the  sense  that  they  cannot  be  directly  overcome. 

265 


266  SOURCES  OF  EFFICIENCY 

But  a  knowledge  even  of  these  insuperable  restrictions  is  often  an 
aid  to  efficiency  in  certain  ways,  as  in  the  negative  way  of  prevent- 
ing a  waste  of  energy  in  striving  to  overcome  these  deficiencies  by 
direct  methods.  In  other  cases  by  devising  means  by  which  to  over- 
come a  given  limitation  or  part  of  a  limitation,  we  not  only  suc- 
ceed in  diminishing  or  removing  the  deficiency,  but  may  obtain 
additional  results  or  increases  in  efficiency.  In  other  words  one  of 
the  most  important  kinds  of  efficiency  is  the  negative  efficiency  which 
consists  of  the  removal  of  waste,  loss,  error,  and  limitations  of  cer- 
tain kinds.  This  negative  efficiency  is  often  accompanied  by  a 
dialectic  of  positive  efficiency.  Casual  references  to  these  facts  have 
been  made  in  the  preceding  chapters.  We  shall  now  isolate  this 
principle  of  limitation  in  a  measure,  and  concentrate  attention  upojta; 
it,  in  order  as  far  as  possible  to  avoid  the  losses  and  increase  the 
efficiencies  connected  with  it. 

CLASSIFICATION 

Limitations  in  Various  Objects 

Considered  with  reference  to  the  category  of  efficiency  every  object 
is  limited  in  many  ways.  For  example  every  given  kind  of  matter 
is  limited  as  to  the  amount  of  it  which  is  accessible  to  man.  Two 
bodies  of  matter  (as  matter  is  ordinarily  understood)  cannot  occupy 
the  same  space  at  the  same  time.  Matter  cannot  be  created  or 
destroyed.  Each  particular  kind  of  matter  also  has  its  characteristic 
limitations  with  respect  to  density,  combustibility,  fusibility,  and  to 
magnetic,  electric,  luminous,  and  other  physical  properties.  Hence 
each  kind  of  matter  is  restricted  in  efficiency  power,  and  in  its 
efficiental  functions  as  in  the  kinds  of  reuse,  groupability,  and  direc- 
tive it  is  capable  of,  or  can  aid  in. 

In  like  manner  the  force  of  energy  of  any  kind  that  is  accessible 
to  us  is  limited  in  amount.  Transformations  of  energy  are 
hemmed  in  in  various  ways.  For  instance,  when  the  energy  in  coal 
is  converted  into  motion  by  the  use  of  the  steam  engine,  nine-tenths 
of  this  energy  is  lost.  Innumerable  attempts  have  been  made  to 
find  a  way  of  converting  coal  directly  into  electricity,  but  all  have 
been  failures.  A  more  general  limitation  in  this  respect  is  what  is 
termed  dissipation  of  energy,  or,  to  use  a  more  popular  expression, 
the  impossibility  of  perpetual  motion.  The  efficiency  of  many 
processes  is  greatly  restricted  by  the  fact  that  only  a  certain  amount 


LIMITATION  ,  267 

of  energy  can  be  stored  in  a  given  bulk  of  fuel,  or  in  the  core  of  an 
electro-magnet,  or  in  a  storage  battery.  Also  physical  energy,  like 
matter,  can  neither  be  created  or  destroyed. 

Living  organisms  are  subject  both  to  the  limitations  of  the  matter 
and  energy  composing  them,  and  to  other  limitations  peculiar  to 
themselves  as  living  objects.  Thus  protoplasm  is  limited  as  to  the 
speed  with  which  it  can  assimilate  sunshine  and  food,  the  amount 
of  each  which  it  can  absorb,  and  the  ways  in  which  it  can  trans- 
form what  it  absorbs.  Hence  organisms  are  limited  as  to  the  size 
which  they  can  attain  and  their  various  efficiency  properties.  These 
facts  are  recognized  in  such  proverbs  as  ''You  can't  get  blood  out  of 
a  turnip",  and  the  query  "Can  a  leopard  change  his  spots?"  The 
limitations  in  the  efficiency  properties  of  vegetation  are  illustrated  by 
the  fact  that  after  the  saccharine  matter  in  the  sugar  beet  reaches 
about  18  per  cent  of  the  entire  beet,  further  increase  is  apparently 
impossible  owing  to  the  fact  that  the  ordinary  vegetative  processes 
in  the  beet  break  down  when  more  sugar  is  present.  Man,  the  most 
efficient  of  organisms,  is  limited  in  the  speed  with  which  he  can  walk, 
run,  or  perform  any  act,  in  his  ability  to  replace  a  lost  member,  to  in- 
crease his  bodily  height  or  his  length  of  life.  In  fact  every  specific 
quality  of  living  organisms  is  hemmed  in  by,  and  in  one  aspect  means 
restrictions  of  various  sorts. 

Similarly  psychic  powers  are  limited  in  man  and  to  a  much  greater 
extent  in  other  organisms.  Thus  in  the  human  mind  we  find  many 
limitations  with  respect  to  perception,  memory,  imagination,  reason, 
volition,  and  emotion.  For  instance  the  number  of  distinct  objects 
which  one  can  hold  in  his  field  of  vision  at  one  time  is  limited  to 
five  or  six.  The  limitations  in  the  reasoning  and  imaginative  powers 
of  the  ordinary  man  are  made  evident  by  comparing  him  with  the 
genius.  Perhaps  the  most  important  psychic  limitations  for  our 
purposes  are  man's  circumscribed  powers  of  conceiving  and  using 
groups  and  other  fundamental  efficiency  instruments.  Probably  most 
other  psychic  limitations  may  be  in  large  measure  reduced  to  or 
expressed  in  terms  of  these  more  primary  limitations. 

The  kinds  of  limitations  which  have  been  mentioned  thus  far  are 
necessarily  present  in  some  form  in  the  social,  political,  religious, 
industrial,  educational,  artistic,  and  similar  worlds.  Each  of  these 
fields  also  has  its  specific  limitations.  For  example  each  particular 
form  of  government  has  its  own  inherent  defects.     The  same  re- 


268  SOURCES  OF  EFFICIENCY 

mark  applies  to  each  individual  kind  of  music,  or  musical  instrument. 
The  time  required  for  a  given  educational  process  cannot  be  dimin- 
ished beyond  a  certain  point. 

Limitations  in  Abstract  Fields 

Important  cases  of  inhibition  are  also  found  in  more  abstract 
fields.  Thus  space  as  we  ordinarily  understand  the  term,  is  re- 
stricted in  the  number  of  its  dimensions  and  in  many  of  its  proper- 
ties. For  example  only  one  straight  line  can  pass  through  two  given 
points,  and  a  triangle  cannot  have  the  sum  of  two  of  its  sides 
less  than  the  third  side.  The  circle  cannot  be  squared  by  the  use 
of  the  straight  edge  and  compasses. 

Similarly  numbers  have  their  characteristic  limitations.  Prime 
numbers  cannot  be  factored,  and  two  plus  two  cannot  equal  five. 

Time,  in  the  conventional  meaning  of  the  term,  is  limited  to  a 
single  dimension,  and  also  with  respect  to  certain  forms  of  control. 
Thus  we  canijot  recall  the  past  so  as  to  live  it  over  again  and  change 
its  content. 

Closely  related  to  this  are  certain  restrictions  of  order.  To  quote 
a  familiar  illustration,  we  cannot  unfry  an  ^gg.  So  the  inverse  of  a 
process  is  often  more  difficult  than  the  direct  form.  An  example  is 
the  process  of  the  division  of  numbers  as  compared  with  that  of 
multiplication.  In  some  cases  the  inverse  is  easier  than  the  direct 
process;  for  instance,  a  house  can  be  burned  down  more  readily 
than  it  can  be  built. 

Limitations  in  speed  are  often  of  primary  importance  in  an 
efficiency  process. 

Every  species  of  quality  hdiS  its  characteristic  limitations  or  cir- 
cumscriptions. A  soil  that  is  fitted  to  raise  one  kind  of  crop  is 
by  that  very  fact  unfitted  to  raise  certain  other  kinds  of  produce. 
Gases  are  unfitted  to  perform  certain  of  the  functions  of  solids  and 
vice  versa.  In  fact  the  expression  "it  has  the  defects  of  its  quali- 
ties" is  a  common  proverb.  A  man  who  is  especially  qualified  for  one 
kind  of  work  is  often  by  that  very  fact  unfitted  for  another  kind. 

Similarly  each  of  the  primary  instruments  of  efficiency  has  its 
own  special  limitations  or  defects,  many  of  which  correspond  to 
characteristic  useful  properties.  These  have  been  discussed  in 
more  or  less  detail  in  the  preceding  chapters. 


LIMITATION  269 

Forms  of  Limitation 

Thus  far  we  have  grouped  limitations  according  to  the  materials 
or  objects  in  which  they  occur.  It  is  also  useful  to  classify  them 
according  to  certain  characteristic  forms. 

Thus,  with  respect  to  the  categories  of  space  and  quantity,  re- 
strictions may  be  large  or  small;  may  be  scattered  or  compact; 
and  may  occupy  various  positions,  the  most  important  being  an 
apexal  or  commanding  one. 

As  to  the  category  of  force,  the  most  important  distinction  is  that 
between  passive  and  active  limitations.  Among  the  former  are 
those  which  take  the  forms  of  resistance  or  inertia.  Among  the 
latter  are  those  which  manifest  themselves  aggressively  and  which 
often  assume  such  individual  forms  as  disease,  wickedness,  insanity, 
or,  in  general,  what  is  termed  evil. 

Aggressive  limitations  are  often  closely  associated  either  with 
some  form  of  actual  personality  as  with  individuals  who  are  igno- 
rant or  wicked,  or  with  personality  used  in  a  more  or  less  symbolic 
sense,  as  when  we  speak  of  imps,  goblins,  devils,  the  father  of 
lies,  the  beast,  or  the  evil  one. 

Also  with  respect  to  personality  limitations  may  be  classified  as 
subjective  or  objective. 

It  may  also  be  well  to  note  at  this  point  that  limitations  often 
occur  in  a  reciprocal  form.  For  example  in  certain  states  of  mind 
feeling  and  perception  (or  reasoning)  restrict  each  other.  More 
generally,  specificality  and  generality  (i.e.,  intension  and  extension) 
have  reciprocally  inhibitive  powers. 

Grouped  Limitations 

Limitations  also  occur  in  certain  combined  or  grouped  forms. 
For  example  several  limitations  combine  to  prevent  the  perfecting  of 
the  telescope  lens,  among  these  being  chromatic  aberration,  spheri- 
cal aberration,  variations  in  the  density  and  the  chemical  properties 
of  a  piece  of  glass,  and  instability  in  temperature.  More  familiar  in- 
stances are  the  groups  of  limitation  found  in  any  one  person,  or  form 
of  government. 

A  given  limitation  is  often  the  resultant  of  a  number  of  compo- 
nent or  contributing  restrictions.  Thus  the  limitation  in  the  rapidity 
with  which  a  man  can  run  a  given  distance  is  determined  by  the 
limitations  in  his  height,  in  heart,  muscle,  and  nerve  action,  and  in 
his  power  to  store  and  to  give  out  energy  rapidly. 


270  SOURCES  OF  EFFICIENCY 

Similarly  limitations  often  occur  as  multiplicatively  grouped  aggre- 
gates. For  examples  the  limitation  in  the  intensity  of  sunlight  gives 
rise  to  a  whole  system  of  other  limitations,  such  as  those  in  the 
size  of  crops,  in  the  closeness  of  human  associations,  and  the  rate 
of  human  progress.  Each  of  these  in  turn  produces  its  own  distinct 
set  of  restrictions.  Or  viewed  by  the  method  of  analysis  the  limi- 
tation in  the  number  of  bushels  of  wheat  which  can  be  grown  on  one 
acre  of  land  is  due  to  the  diffused  nature  of  sunshine,  the  limited 
powers  of  matter,  force,  and  protoplasm,  and  defects  in  human 
knowledge  and  directive  action.  Again  the  limitation  in  the  power 
of  sunshine  is  the  resultant  of  a  number  of  more  elemental  limita- 
tions such  as  those  in  the  nearness  of  the  sun,  in  the  temperature 
of  the  sun's  surface,  and  in  the  angle  at  which  the  sun's  rays  fall 
on  the  earth.  Similarly  each  of  these  restrictions  could  be  resolved 
into  a  group  of  constituents.  A  still  larger  multiplicative  group 
system  of  limitations  could  be  obtained  by  analyzing  the  slowness  of 
human  progress  into  its  causes. 

Scales  of  Limitation 

As  a  result  it  follows  that  limitations  may  often  be  arranged  in 
an  order  of  materials  scale.  A  limitation  may  be  of  a  high  order 
owing  to  the  fact  that  it  occupies  an  apexal  position  in  a  multipli- 
cative group  system  of  limitations,  an  example  being  a  limitation  in 
human  knowledge;  or  owing  to  the  fact  that  it  is  a  limitation  in 
some  material  or  object  of  a  high  order.  Thus  a  serious  lack  of 
some  kind  in  the  president  of  the  United  States  may  check  the 
development  of  the  whole  nation. 

Relative  and  Absolute  Limitations 

The  most  important  distinction  in  this  connection  is  that  between 
relative  and  absolute  limitations.  Some  restrictions  seem  to  be 
ultimate  and  beyond  human  control,  while  others  are  only  superficial, 
contingent,  or  apparent.  Examples  of  the  absolute  species  are 
human  inability  to  raise  the  dead  to  life,  or  the  logical  limitation  in 
the  number  of  sides  of  a  triangle.  Examples  of  the  relative  are 
limitations  in  human  efficiency  due  to  certain  preventable  diseases, 
as  yellow  fever  or  malaria. 

An  important  form  of  relative  limitation  is  that  which  exists  only 
with  reference  to  certain  other  limitations.  Thus  in  a  factory  it 
may  be  possible  to  run  a  given  machine  with  much  greater  rapidity 


LIMITATION  271 

than  is  actually  used,  but  it  may  not  pay  to  do  so  owing  to  the 
limitations  in  the  speed  of  other  processes  in  the  establishment.  Gold 
exists  in  vast  quantities  ii;i  sea  water,  but  it  does  not  pay  to  extract 
it  at  present  owing  to  the  greater  efficiency  of  other  methods  of 
obtaining  this  metal,  and  also,  perhaps,  to  the  limitations  in  our 
knowledge  of  the  best  way  to  extract  this  gold.  The  interior  heat 
of  the  earth  cannot  at  present  be  profitably  utilized  by  man  owing 
to  the  fact  that  tunnels  to  reach  this  heat,  and  make  it  practically 
available  would  cost  at  least  $25,000,000.  But  at  some  later  stage  in 
the  world's  history  it  may  be  profitable  to  make  even  this  expenditure. 
In  allowing  for  limitations  in  connection  with  efficiency  processes, 
it  is  important  to  remember  that  restrictions  of  various  kinds  may  be 
compounded  and  complexed  in  many  intricate  ways.  Among  the 
most  important  cases  of  complex  limitation  are  those  which  are 
cumulative  in  form.  As  an  illustration  we  have  the  limitations 
which  accumulate  progressively  in  the  successive  fields  of  matter, 
force,  life,  mind,  society,  and  education. 

EFFICIENCY  RELATIONS  OF  LIMITATION 

It  will  be  an  aid  to  efficiency  in  important  ways  to  observe  certain 
facts  with  reference  to  the  nature  of  limitation. 

Limitations  are  Multiplicative 

In  the  first  place  it  is  important  to  realize  that  various  limitations, 
in  the  vast  majority  of  cases,  are  not  scattered,  discordant,  or  acci- 
dental in  their  relations,  but  on  the  contrary  are  connected  in  multi- 
plicative systems.  For  instance  there  exist  certain  vital  and  primary 
limitations,  such  as  ignorance,  each  of  which  includes  many  second- 
ary and  derived  cases. 

It  follows  that  limitation  is  not  primarily  a  lumpish,  blind,  and 
inert  something,  but  that  it  is  normally  active  and  aggressive,  and  that 
different  forms  of  it  often  combine  to  act  in  sudden  and  overwhelm- 
ing ways.  An  example  is  the  loss  of  the  steamship  Titanic  in  the 
year  1912. 

Sources  of  Efficiency  in  Limitations 

In  naming  and  treating  a  given  case  as  primarily  a  case  of  limita- 
tion, a  certain  human  element  is  often  present.  This  often  proves  a 
serious  hindrance  in  the  efficient  treatment  of  such  cases,  though  in 


2^2  SOURCES  OF  EFFICIENCY 

some  it  is  a  help.  The  thorn  on  the  rose  having  pricked  us,  we 
regard  the  thorn  as  a  drawback  or  Hmitation  to  the  beauty  of  the 
rose,  without  stopping  to  consider  the  utiHty  of  the  thorn  as  a  pro- 
tection to  the  rose  under  certain  circumstances,  and  its  consequent 
value  in  the  general  scheme  of  things.  So  in  general  limitation 
from  the  broader  point  of  view  is  often  entirely,  always  perhaps  in 
part,  mere  diversity,  our  unpleasant  feeling  concerning  it  coming 
largely  from  narrow  personal  associations.  In  certain  other  aspects 
limitation  is  that  which  helps  form  units  and  even  the  Efficients  them- 
selves. Friction  and  inertia  are  often  disagreeable,  but  they  enable 
us  to  walk,  to  weave  materials  together  as  cloth,  and  to  make  many 
other  groups  and  multiplicative  groups. 

In  connection  with  the  fact  that  limitation  is  in  some  respects 
diversity  viewed  in  a  certain  personal  way,  the  nearness  of  these  twa 
sides  of  the  matter  should  be  noted.  From  this  it  follows  that 
wherever  a  so-called  limitation,  or  even  evil  appears,  some  utility 
must  be  very  close  at  hand.  The  defects  of  qualities  and  qualities 
themselves  are  in  immediate  contact.  Often  also  the  greater  the 
limitation  the  greater  the  potential  efficiency  associated  with  it.  The 
fact  that  Faraday  lacked  an  extensive  knowledge  of  technical  mathe- 
matics left  his  mind  free  to  take  certain  large  and  fundamental 
steps  and,  in  effect,  invent  a  new  theory  of  the  matter  and  ether, 
and  discover  among  other  things  the  principle  of  the  dynamo. 
Graham  Bell  knew  just  enough  of  electricity  to  enable  him  to  take 
the  bold  step  which  an  expert  electrician  would  have  hesitated  to 
take  and  which  resulted  in  the  making  of  the  telephone. 

EFFICIENCY   METHODS   OF   TREATING   LIMITATION 

Externality  the  Best  General  Method 

It  has  already  been  stated  that  the  best  general  method  of  treating 
cases  of  limitation  is  by  the  use  of  externality ;  that  is,  by  taking  a 
larger  view  of  things,  so  as  readily  to  perceive  such  efficiency 
aspects  of  co-called  limitations  as  diversity,  units  and  their  multi- 
pliers, groups,  or  more  generally  the  fundamentally  multiplicative 
nature  of  limitation  and  its  relation  to  the  multiplicative  scheme  of 
things.  However,  just  as  there  is  a  whole  scale  of  degrees  of  limita- 
tion, so  there  is  a  scale  of  degrees  and  kinds  of  externality  which  to 
apply,  with  a  variety  of  special  forms  of  efficiency  as  a  result. 


LIMITATION  273 

Treatment  of  Difficult  Cases 

In  the  first  case,  some  forms  of  limitation  are  so  fundamental  and 
stubborn  that  only  remote  and  indirect  externalities  can  be  applied 
to  them  as  a  means  of  remedying  and  overcoming  them,  and  perhaps 
obtaining  other  more  positive  efficiency  results.  A  ton  of  coal  once 
burned  cannot  be  burned  again.  But  if  the  energy  obtained  by  burn- 
ing the  coal  be  stored  in  some  permanently  useful  shape,  as  in  a 
manufactured  machine,  or  as  ideas  worked  out  while  the  thinker  is 
sustained  by  heat  given  off  during  the  combustion,  the  energy  in  the 
coal  may  be  reused  and  the  coal  in  a  manner  be  said  to  be  recon- 
sumed.  Life  may  be  prolonged  indefinitely  in  the  sense  that  the 
mind  can  forecast  and  in  a  measure  anticipate  many  of  the  experi- 
ences of  the  future.  Often  the  externality  applicable  to  the  class 
of  restrictions  under  consideration  takes  the  form  of  mere  patience. 

A  knowledge  of  limitations  also  has  important  efficiency  uses 
even  when  we  do  not  attempt  to  overcome  the  given  restrictions.  If 
the  given  prohibitions  are  fundamental  and  insuperable  along  certain 
channels,  we  are  saved  the  losses  of  various  kinds  which  must  follow 
an  attempt  to  overcome  limitations  in  such  ways.  Thus  a  knowledge 
that  the  circle  cannot  be  squared  by  the  use  of  the  ruler  and  com- 
passes, saves  us  the  loss  of  time  and  energy  involved  in  attempting 
thus  to  square  it.  In  this  case  the  externality  involved  is  that  of  a 
large  view  of  the  aims  and  ends  of  action  and  of  the  means  of 
attaining  these  aims,  and  the  use  of  a  totally  new  channel  in  reach- 
ing a  large  measure  of  positive  non-equivalence. 

Some  Limitations  a  Direct  Source  of  Efficiency 

The  limitations  surrounding  an  object  or  domain  are  often  better 
known  or  easier  to  grasp  than  the  object  itself,  and  hence  form  a 
convenient  externality  by  which  to  deal  with  the  object  or  subject 
in  hand.  Thus  it  is  often  easier  to  understand  and  deal  with  a  man 
by  observing  what  he  is  not  or  by  his  mistakes  than  by  his  direct 
qualities.  Of  a  similar  efficient  nature  are  the  proofs  by  exclusion  as 
used  in  logic  or  mathematics.  Similarly  it  is  a  well  known  fact  that 
in  the  human  body  a  set  of  nerves  of  a  given  kind  is  held  in  check  by 
another  set,  and  that  often  the  best  way  to  stimulate  a  man  is  tem- 
porarily to  paralyze  the  inhibiting  nerves  to  some  degree.  Or  in 
general  the  most  advantageous  way  of  making  a  person  or  domain 
efficient  may  be  merely  to  sever  a  set  of  restraining  bonds.     It  is 


274  SOURCES  OF  EFFICIENCY 

evident  that  this  use  of  negative  externality  may  be  built  up  in 
multiplicative  group  fashion. 

So  in  general  all  increases  of  efficiency,  in  one  aspect,  are  obtained 
by  a  removal  of  waste,  ignorance,  or  other  limitation;  that  is,  all 
positive  efficiency  has  a  negative  aspect.  This  negative  aspect  is 
often  the  more  accessible  and  manageable  of  the  two. 

A  Cause  of  Dialectic 

Of  somewhat  similar  nature  are  those  instances  where  a  lack  of 
one  desirable  quality  leads  to  the  development  of  other  and  often 
more  desirable  ones.  An  illustration  is  the  case  of  a  woman  who, 
owing  to  a  deficiency  in  physical  beauty,  is  led  to  the  development  in 
high  degree  of  mental  powers  and  a  spirit  of  service.  Often  the 
wide  and  deep  externality  thus  called  into  play  leads  to  an  impor- 
tant dialectic  of  results.  For  example  the  fact  that  our  organs  of 
speech  can  make  only  a  limited  number  of  distinct  sounds  has  com- 
pelled men  to  reuse  these  organs  in  various  ways,  as  in  various  order 
groups,  thus  producing  the  group  system  of  articulate  speech.  This 
smallness  of  the  number  of  primal  units  of  speech  has  led  to  other 
efficiencies  such  as  the  invention  of  the  phonetic  alphabet,  the 
typewriting  machine,  the  Morse  and  other  like  alphabets  with  their 
many  applications.  So  the  limitation  in  the  amount  of  available 
gold  in  the  world  has  resulted  in  the  wide  use  of  symbols  such  as 
paper  money  and  checks  to  represent  this  gold  and  as  a  consequence 
to  great  economics  and  efficiencies  in  commercial  processes.  Simi- 
larly a  difficulty  or  defect  often  calls  into  action  latent  efficiency 
powers  either  in  an  individual  or  a  social  organization.  An  example 
is  the  effect  produced  in  Germany  by  the  conquests  of  Napoleon. 

We  next  consider  cases  of  limitation  which  may  be  remedied  in 
some  indirect  way  and  often  thus,  from  one  point  of  view,  made  the 
source  of  higher  efficiencies.  An  example  is  limitation  in  human 
vision  as  overcome  by  the  lens.  It  is  to  be  observed  that  the  first 
use  of  the  lens  in  the  telescope  to  overcome  deficiencies  due  to  dis- 
tance has  brought  with  it  a  dialectic  of  results  illustrated  by  the  use 
of  the  lens  in  the  microscope,  and  of  the  latter  in  the  investigation 
of  malaria,  tuberculosis,  and  Hke  diseases. 

Applications  of  Externality 

The  externalities  applied  in  such  cases  frequently  takes  many  im- 
portant special  forms.     Often  a  wide  survey  of  material  reveals 


LIMITATION  275 

certain  spots  where  a  difficulty  disappears,  and  light  or  power  which 
can  be  reused  in  important  ways  becomes  prominent.  Thus  both 
Darwin  and  Wallace  by  travelling  and  observing  widely  chanced 
upon  facts  which  clearly  indicated  the  variation  of  species,  and  which 
when  fully  interpreted  gave  the  theory  of  evolution.  Similarly  a 
wide  grouping  of  facts  by  the  Baconian  method,  although  applied 
first  to  the  removal  of  difficulties,  has  often  ultimately  led  to  scien- 
tific discoveries  and  inventions  of  direct  value. 

Another  way  in  which  it  is  often  advantageous  to  use  externality 
is  to  allow  an  evil  or  limitation  to  develop  its  own  consequences,  and 
thus  bring  its  own  cure  in  whole  or  part.  This  process  is  often 
efficient  by  virtue  of  the  fact  that  it  arouses  the  attention,  and 
utilizes  the  hitherto  inert  powers  of  a  large  number  of  more  or  less 
unoccupied  persons.  As  has  already  been  pointed  out,  it  is  often  a 
source  of  efficiency  to  allow  this  method  to  take  the  form  of  alter- 
nate dialectic  and  directive. 

Personifying  evils  and  limitations  (that  is,  annexing  the  extern- 
ality of  personality  to  them),  as  when  we  speak  of  the  works  of 
imps,  goblins,  and  devils,  often  forms  an  effective  method  of  sum- 
ming up  and  making  vivid  the  tendency  and  results  of  a  given  evil, 
and  of  arousing  powers  which  will  overcome  it.  This  method 
however  has  compensating  drawbacks. 

Overcoming  Limitations  in  Groups 

A  much  more  important  principle  in  this  connection  is  that  of 
taking  such  a  comprehensive  view  of  matters  as  to  be  able  to  remove 
limitations  and  evils  in  groups,  as  by  overcoming  some  deep-seated 
limitation  which  is  the  source  of  many  more  superficial  ones.  An 
example  is  the  removal  of  many  forms  of  -disease,  much  poverty, 
ignorance,  vice,  and  unhappiness  in  a  city  by  improving  its  sanitary 
condition  and  by  the  education  of  its  children. 

Often,  in  overcoming  limitations  in  groups,  many  forms  of 
externality  are  used  together  which,  beside  overcoming  the  given 
limitations,  bring  added  positive  efficiency  results.  The  Krupp  firm 
in  making  cannon  have  to  overcome  limitations  in  the  properties  of 
iron,  in  the  physical  powers  of  workmen,  and  in  human  knowledge. 
In  doing  this  work  they  employ  coal  and  various  physical  forces, 
manifold  machinery,  and  the  largest  physical  and  chemical  labora- 
tory in  the  world.     But  by  so  doing  they  have  not  only  achieved 


276  SOURCES  OF  EFFICIENCY 

their  immediate  purpose,  but  have  also  discovered  many  mechaincal 
principles  and  scientific  facts  widely  useful  in  the  arts  and  trades. 

Adapted  Treatment  of  Limitation 

Some  species  of  limitation  may  be  regarded  as  relative,  in  the 
sense  that  it  pays  under  some  circumstances  to  submit  to  them  for 
the  time  being,  and  under  others  to  try  to  overcome  them;  that  is, 
at  some  times  to  apply  only  a  remote  and  indirect  externality,  and 
at  others  a  direct  one.  For  instance  in  some  parts  of  the  world  and 
in  some  ways  it  is  a  source  of  efficiency  to  overcome  the  limitations 
of  peat  as  a  fuel,  and  in  others  it  does  not  pay  to  use  peat  in  this 
way.  The  English  system  of  weights  and  measures  in  itself  has 
great  defects  as  compared  with  the  metric  system.  But  it  has  the 
important  property  that  its  very  deficiencies  make  it  homogeneous 
with  the  great  majority  of  efficiency  methods  in  use  the  world 
over.  Hence  its  mastery  furnishes  a  convenient  unit  to  reuse  in 
connection  with  other  processes.  The  same  remark  applies  to  the 
systems  of  spelling  and  pronunciation  which  characterize  the  English 
language.  Perhaps  the  great  practical  power  of  the  English  and 
American  peoples  may  be  due,  in  a  measure,  to  their  training  in  these 
and  similar  disciplines.  At  the  same  time  the  English  speaking  man 
of  science  in  his  private  work  does  not  hesitate  to  set  aside  the 
English  system  of  weights  and  measures  for  the  more  convenient 
metric  system. 

Similarly  the  wise  man  recognizes  and  submits  to  his  personal 
limitations. in  selecting  a  field  of  life  work.  At  the  same  time,  under 
many  special  circumstances  he  tries  to  overcome  these  limitations  as 
far  as  possible,  A  wider  illustration  of  this  principle  is  the  whole- 
some moderation  which  was  characteristic  of  the  Greeks  in  all  their 
process  of  life,  and  by  which  they  were  able  to  attain  such  vast  and 
permanent  results.  So,  in  general,  sacrifice  and  restraint,  in  some 
respects,  are  necessary  to  broad  and  vital  efficiency  processes  of  any 
sort. 

Value  of  Exact  Knowledge 

At  this  point  becomes  especially  evident  the  value  of  the  exact 
knowledge,  quantitative  as  far  as  possible,  of  the  various  species  and 
forms  of  limitations.  Vast  amounts  of  such  knowledge  are  found  in 
various  technical  treatises  on  the  different  sciences  and  arts.    Each 


LIMITATION  -  277 

man  in  his  particular  field  can  often  determine  other  more  special 
and  detailed  limitation  facts  as  to  his  work.  Thus  Mr.  F.  W. 
Taylor  in  his  investigations  which  led  to  the  system  of  efficiency 
which  he  calls  scientific  management,  has  found  that  work  in  certain 
shops  is  most  efficient  when  each  planner  or  overseer  has  under  him 
not  more  than  three  men  on  the  average,  and  that  a  shovel  load 
for  a  common  laborer  should  not  exceed  21  pounds.  In  general  if 
the  boundary  facts  are  known  in  any  line  or  department  of  human 
knowledge  or  action,  it  is  possible  to  construct  with  confidence  the 
largest  available  or  practical  multiplicative  group  or  order  of  mater- 
ials system  in  that  domain,  with  a  view  to  varying  from  this  by 
marginal  reuse  from  time  to  time  according  to  circumstances. 

In  this  connection  it  is  also  well  to  note  that  in  every  situation  a 
residuum  of  work  by  somebody  is  always  necessary,  and  that  it 
often  does  not  pay  to  try  to  remove  all  of  removable  limitation, 
but  that  better  results  are  obtained  by  working  partly  in  other 
lines.  Similarly  instead  of  working  with  great  rapidity  in  a  single 
line,  it  often  pays  better  to  work  at  a  more  moderate  rate  in  several 
directions. 

From  the  preceding  discussion  it  is  evident  that,  in  discriminating 
between  cases  of  limitation  and  also  for  general  purposes,  it  is  an 
important  source  of  efficiency  to  keep  in  mind  the  multiplicative 
nature  of  limitation.  This  facilitates  an  appreciation  of  the  many 
forms  which  limitation  may  assume,  the  extreme  nature  of  some  of 
these,  the  grasp  of  them  as  a  tabulated  whole,  and  the  marginal  reuse 
and  more  general  group  methods  of  treating  them. 

Two  Opposed  Systems 

Hence  the  best  way  to  treat  limitation  as  a  whole  is  to  consider  it, 
not  in  an  isolated  fashion,  but  in  connection  with  the  general  system 
of  efficiency  and  surplusage,  and  to  regard  the  two  principles  (of 
gain  and  limitation)  as  two  opposed  multiplicative  systems;  not  to 
neglect  or  ignore  parts  of  the  two  systems  which  seem  to  cancel 
each  other,  but  to  regard  the  two  opposed  systems  as  always  existent 
and  in  action.  Thus  in  psychology  the  process  of  forgetting  is  not 
to  be  regarded  as  a  mere  erasure  of  mental  data,  but  as  due  to  the 
encroachment  of  one  multiplicative  mental  grouping  upon  another. 
The  same  ultimate  two-systemed  conception  of  things  is  found  in  a 
crude  form  in  the  doctrine  of  total  depravity  along  with  that  of  divine 


278  SOURCES  OF  EFFICIENCY 

grace  in  certain  theologies.  In  all  cases  however  in  dealing  with  two 
opposed  systems  the  positive  or  useful  system  is  to  be  regarded  as 
dominant  over  the  negative  one. 

This  general  combination  concept  often  takes  various  special 
forms.  Thus  it  is  frequently  an  advantage  to  conceive  of  it  in  the 
form  of  a  rhythm  in  which  the  main  action  is  that  of  positive  multi- 
plication, while  the  negative  part  consists  of  mere  back  eddies.  The 
advantage  in  this  method  of  viewing  the  matter  is  that  it  facilitates 
the  application  of  dialectic  in  taking  care  of  the  limitations 
involved. 

Other  Uses  of  the  Two  Opposed  Systems 

Similarly  the  more  general  conception  of  two  opposed  multiplica- 
tive systems  brings  important  efficiental  values.  For  it  provides  an 
endless  store  of  diversities  and  varied  reciprocal  externalities  to 
be  utilized  in  efficiency  processes.  In  Germany  where,  at  the  present 
time,  in  many  respects,  scientific  efficiency  has  reached  its  highest 

development,  it  is  estimated  that  only  — —  part  of  the  sun  force 

which  falls  on  a  cultivated  field  is  collected  in  a  useful  form  by  the 
crops  produced.  When  we  consider  the  great  array  of  efficiency 
processes  which  are  here  applied,  we  realize  the  vast  extent  and 
power  of  the  limitations  at  work.  We  get  a  more  comprehensive 
view  of  these  when  we  consider  that  the  world  as  a  whole  is  moving 
forward  only  at  a  snail's  pace  with  back  eddies  some  of  them  tens  of 
centuries  long.  We  may  thus  realize  to  some  extent  the  enormous 
results  which  it  is  possible  to  attain  by  a  mere  negating  of  limitation 
as  well  as  the  extent  of  more  positive  opportunities.  In  this  connec- 
tion it  may  also  be  noted  that  the  greatness  of  a  difficulty,  or  even 
defeat,  often  is  a  measure  of  the  greatness  of  the  related  opportunity. 
The  double  multiplicative  view  of  limitation  both  prevents  a  raw  and 
unlimited  optimism  and  inculcates  a  sane,  wholesome,  and  discrim- 
inating optimism. 

The  most  important  general  result  which  follows  from  conceiving 
the  world  as  two  opposite  multiplicative  systems  lies  in  the  fact  that 
the  separation  thus  involved  enables  us  to  conceive  of  an  ideal  goal 
of  human  endeavor,  or,  to  express  the  matter  in  a  more  general 
form,  to  conceive  of  a  summum  bonum  of  all  processes.  For  when 
considered  apart  from  limitation,  the  positive  surplusage  treated  in 


LIMITATION  279 

Chapter  IX  becomes  unlimited  in  amount  and  quality  for  each  per- 
son and  entity;  or  in  other  words  each  person  and  conscious  entity 
would  have  a  near  and  instant  and  unlimited  wealth  and  ecstasy. 

Summary  of  Chapter 

To  sum  up  the  chapter,  a  fundamental  but  somewhat  indirect 
source  of  efficiency  is  that  of  studying  the  limitations  of  a  given 
process,  determining  whether  these  limitations  are  fundamental  or 
superficial,  and  devising  means  to  overcome  them  as  far  as  possi- 
ble. It  is  advantageous  to  classify  limitations  both  according  to 
the  objects  or  fields  in  which  they  are  found,  and  also  according 
to  the  forms  which  they  assume.  Special  mention  may  be  made  of 
the  species  of  limitation  respectively  termed  active,  passive,  abso- 
lute, relative,  grouped,  or  complex,  since  a  knowledge  of  each  of 
these  is  an  important  special  source  of  power.  It  is  also  important 
to  realize  whether  each  given  limitation  is  personal  and  subjective, 
or  objective.  It  is  also  at  times  an  aid  to  new  results  to  understand 
that  a  limitation  is  essentially  a  diversity,  and  hence  may  be  made 
the  source  of  those  fruitages  which  are  characteristic  of  diversities. 

The  principle  of  externality  supplies  the  best  method  both  for 
the  accurate  determination  of  limitations,  and  also  for  the  advan- 
tageous treatment  of  them.  It  is  evident  also  that  varioUis  adapted 
species  of  externality  should  be  applied  to  difficult  kinds  of  limita- 
tion. Hence  the  value  of  thorough  and  exact  knowledge  in  every 
field  of  operation.  The  most  general  and  useful  conception  in 
dealing  with  any  large  domain  of  material  is  that  of  efficiency  and 
limitation  acting  in  the  domain  as  two  comprehensive  and  opposed 
multiplicative  systems. 


EXERCISE  17 

1.  Give  an  example  of  each  of  the  principal  kinds  of  limitation. 

2.  The  limitation  of  the  speed  of  a  railroad  train  is  the  resultant  of  what 
component  limitations  ? 

3.  It  is  said  that  the  clay  which  underlies  the  city  of  Philadelphia  contains 
over  $125,000,000  worth  of  gold.  State  some  of  the  reasons  why  this  gold 
cannot  be  utilized. 

4.  It  is  estimated  that  one  ton  of  radium  would  drive  a  15,000  ton  ship 
for  thirty  years  at  a  speed  of  15  knots  per  hour.  Why  is  not  radium  used  for 
propelling  steamships  ? 


28o  SOURCES  OF  EFFICIENCY 

5.  State  three  cases  in  which  friction  is  a  limitation  to  human  activity, 
and  also  three  in  which  it  is  an  aid. 

6.  Name  some  noted  man  the  limitations  of  whose  childhood  have  helped 
make  him  great. 

7.  Show  that  the  limited  amount  of  food  in  the  world  has  had  the  effect 
of  making  the  forms  of  animal  life  on  the  earth  more  efficient. 

8.  Give  an  illustration  of  the  difference  between  a  real  and  an  apparent 
limitation. 

9.  Show  how  the  phrase   "defects  of  its   qualities"   is  illustrated  by  the 
properties  of  water. 

10.  Of  iron  11.  Of  electricity  12.  Of  money 

13.  Give  a  case  where  the  limitations  of  an  object  are  easier  to  recognize 
and  to  use  than  the  object  itself. 

14.  If  the  efficiency  of  man's  body  when  used  as  a  machine  is  21  per  cent 
and  that  of  a  small  steam  engine  is  3  per  cent,  compare  the  two  efficiencies. 
What  means  are  there  of  overcoming  the  limitations  involved  in  each 
case? 

15.  If  a  large  steam  engine  is  10  per  cent  efficient,  while  a  small  one  is  1.5 
per  cent  efficient,  state  the  degrees  of  relative  efficiency  involved,  and  also  the 
sources  of  greater  efficiency  in  the  large  engine. 

16.  If  a  steam  engine  is  10  per  cent  efficient  and  a  gas  engine  ^  efficient, 
compare  the  efficiencies  involved,  and  state  an  efficiental  terms  some  of  the 
sources  of  the  difference. 

17.  Compare  the  relative  advantages  and  disadvantages  in  having  a  building 
erected  by  contract  and  by  day's  labor. 

18.  State  some  of  the  causes  which  limit  the  amount  of  income  from  a  safe 
investment. 

19.  A  soil  that  is  suitable  for  the  raising  of  sweet  potatoes  is  not  fitted  for 
raising  tobacco  and  wheat.    Give  a  similar  illustration  of  your  own. 

20.  Every  musical  instrument  is  said  to  have  some  characteristic  limitation. 
Name  these  as   far  as  you  can. 

21.  Heat  expands  metal.  Give  an  example  where  this  property  is  useful. 
Another  where  it  is  a  disadvantage. 

22.  Why  is  it  that  the  tides,  as  sources  of  mechanical  power,  are  not  gen- 
erally available  for  human  use?  Answer  the  same  for  the  waves  of  the  ocean. 

23.  Give  an  example  of  an  efficiency  blessing  appearing  in  the  disguise  of  a 
limitation. 

24.  Give  an  example  where  the  use  of  an  externality  not  only  overcomes  a 
given  limitation  but  is  also  a  source  of  positive  efficiency. 

25.  Give  an  illustration  of  the  fact  that  a  wide  survey  of  material  often 
reveals  a  place  or  places  where  a  given  limitation  disappears. 

26.  Give  an  example  where  the  exact  knowledge  of  limitations  has  led  to 
their  more  efficient  treatment. 

27.  Give  an  example  of  a  group  of  limitations  or  evils  which  have  been 
overcome  by  destroying  their  common  root. 


CHAPTER  XVI 
ERROR  AND  PARADOX 
Removal  of  Waste  and  Error  as  a  Source  of  Efficiency 

In  the  preceding  chapter  it  was  stated  that  every  efficiency  process 
from  the  ideal  point  of  view  is  a  mere  removal  or  undoing  of  limita- 
tion or  unnecessary  loss ;  that  is,  every  efficiency  process  has  a  nega- 
tive as  well  as  a  positive  aspect.  It  was  also  pointed  out  that,  in 
obtaining  increased  efficiency  in  a  given  domain,  it  is  often  an  advan- 
tage to  pay  primary  attention  to  this  negative  aspect  which  consists 
of  the  removal  of  limitation.  This  principle  is  of  particular  impor- 
tance with  respect  to  certain  special  kinds  of  limitation.  One  of 
these  is  that  species  of  limitation  where  some  element  of  personality 
is  involved,  as,  for  instance,  in  cases  of  ignorance  and  error.  The 
removal  of  these  is  often  an  especially  valuable  means  of  creating 
or  improving  efficiency.  One  reason  for  this  is  that  a  mistake  is 
something  below  the  general  level  of  current  social  efficiency,  and 
the  manifold  adjacent  social  externality  supplies  abundant  aids  of 
various  kinds  in  remedying  the  given  source  of  loss.  This  applies 
for  instance  to  a  person  of  intemperate  habits  who  lives  in  a  highly 
moral  community,  or  to  a  glass  manufacturer  who  is  melting  his 
glass  in  pots  while  his  neighbors  use  large  tanks  for  the  purpose. 
Another  reason  why  particular  attention  to  the  prevention  and  cor- 
rection of  mistakes  is  a  fruitful  source  of  efficiency,  is  the  fact  that 
direct  efficiency  often  means  merely  added  luxury  and  hence  some- 
thing which  may  be  dispensed  with,  while  a  mistake  may  mean  ruin 
and  the  loss  of  all  essentials.  Hence  awareness  of  error  and  loss 
is  frequently  far  more  stimulating  and  productive  of  the  use  of  all 
possible  factors  and  aids  in  obtaining  results,  than  is  the  mere  concep- 
tion of  new  and  additional  sources  of  profit. 

Further  Advantages 

For  certain  special  reasons  also,  measures  taken  to  prevent  or  to 
correct  errors  are  often  the  source  of  peculiarly  powerful  dialectical 
(i.e.  extra  and  unexpected)  efficiencies.  For  in  case  of  error  we 
are  concerned  with  the  double  fact  that,  objectively,  the  multiplica- 


282  SOURCES  OF  EFFICIENCY 

tive  principle  is  giving  results  so  profuse  that  they  cannot  be  fully 
grasped,  and  also  that,  subjectively,  certain  powers  are  at  work  in 
like  manner,  such  as  the  directive  faculty  or  the  mental  powers  in 
general.  Hence  error  is  best  regarded  in  general  as  the  multiplica- 
tive principle  acting  in  a  special  doubly  errant  way,  or,  in  other 
words,  as  double  misgrouping  of  some  kind.  Socrates  was  persecuted 
and  put  to  death  because  he  was  falsely  classed  with  the  selfish 
destroyers  of  the  national  customs.  Selfishness  is  mainly  due  to  the 
lack  of  externality  and  hence  is  a  form  of  misgrouping.  Errors  in 
the  use  of  words  and  figures  are  simpler  cases  of  misgrouping. 
Hence  the  fundamental  means  of  preventing  and  correcting  errors 
is  the  acquirement  of  a  thorough  knowledge  of  the  group  principle 
in  all  of  its  aspects,  including,  in  particular,  an  aggressive  use  of 
various  kinds  of  externality.  It  is  also  to  be  remembered  that  these 
methods  often  lead  to  a  new  and  vital  dialectic.  As  an  illustration 
we  have  the  fact  that  a  man  who  overcomes  the  habit  of  drunken- 
ness must  usually  acquire  some  ideal,  or  religious  principles,  or  even 
a  new  and  profound  philosophy  of  life,  giving  many  aggressive 
efficiencies  over  and  above  the  mere  correction  of  a  bad  habit.  In 
order  to  obtain  a  quick  detection  and  correction  of  error  and  waste, 
a  business  man  often  devises  some  special  method  of  keeping  ac- 
counts, one,  for  instance,  by  which  any  element  of  his  business  can 
be  summarized  and  balanced  at  the  end  of  each  day.  This  method 
not  only  brings  the  quick  correction  of  errors,  often  in  groups,  but 
the  knowledge  thus  obtained  often  leads  to  the  development  of  new 
and  positive  efficiencies.  Similarly  the  syllogistic  method  of  exam- 
ining a  course  of  reasoning  in  order  to  detect  possible  fallacies, 
frequently  leads  to  a  searching  analysis  of  data  which,  in  the  end, 
begets  a  more  fundamental  and  efficient  multiplicative  grouping  of  a 
given  domain. 

General  Method  of  Investigating  Error 

As  error  always  occurs  in  the  process  of  striving  after  results, 
in  illustrating  the  different  species  of  error  it  will  be  useful  fre- 
quently to  point  out  the  efficiency  principles  which  are  distorted  or 
misused  in  a  given  case.  For  if  a  given  principle  is  found  to  be 
misused  in  many  different  cases,  a  more  correct  use  of  this  principle 
will  lead  to  the  detection,  correction,  and  prevention  of  errors  in 
groups,  with  a  corresponding  intensification  of  dialectic  results. 


ERROR  AND  PARADOX  283 

In  order  to  condense  the  treatment  as  far  as  possible  special  at- 
tention will  be  paid  to  those  extreme  and  persistent  sources  of  error, 
the  mastery  of  which  confers  a  grasp  of  many  lesser  and  more 
superficial  ones. 

CLASSIFICATION 
Different  Fields  of  Error 

The  domain  of  material  in  which  a  given  error  has  been  made 
to  some  extent  determines  the  source  of  the  given  error,  and  also 
the  form  which  the  error  takes.  Hence  in  classifying  errors  accord- 
ing to  material  or  content,  we  shall  also  to  a  certain  extent  be  classify- 
ing them  according  to  source  and  form. 

Important  errors  have  been  made  with  respect  to  inorganic  objects, 
and  the  correction  of  these  mistakes  has  been  the  source  of  far-reach- 
ing efficiencies.  For  instance  for  a  long  time  it  was  regarded  as 
impossible  that  the  addition  of  a  fraction  of  one  per  cent  of  carbon 
to  a  mass  of  iron  would  of  itself  convert  the  iron  into  steel.  The 
correction  of  this  error  has  led  to  vast  improvements  in  the  manu- 
facture of  steel.  A  similar  mistake  was  that  concerning  the  resist- 
ance which  air  makes  to  projectiles.  It  is  to  be  noted  that  the  root 
of  these  errors  was  a  failure  to  grasp  the  extreme  results  which 
follow  from  the  multiplicative  properties  of  matter.  Other  like 
paradoxical  truths  which  have  been  or  may  become  the  sources  of 
efficiency  are  the  fact  that  water  is  more  dense  than  either  of  its 
constituent  gases,  oxygen  and  hydrogen;  that  solder  has  a  lower 
melting  point  than  either  of  its  components,  lead  and  tin;  that  the 
process  of  tempering  hardens  steel  and  softens  copper ;  and  that  the 
diamond  chemically  is  pure  carbon. 

Similarly  we  have  paradoxical  properties  and  corresponding 
errors  concerning  forces.  Illustrations  are  the  fact  that  water  will 
wear  away  a  stone;  that  river  courses  are  often  more  permanent 
than  mountains ;  and  that  gravitation  is  the  feeblest  of  known  forces. 
Surprise  and  error  concerning  these  statements  arise  from  a  failure 
to  realize  that  the  action  of  water  in  the  above  instances  is  a  re- 
peated one,  and  hence  has  a  dimension  not  possessed  by  the 
cohesive  force  which  holds  a  solid  object  together;  and  gravitation, 
as  we  are  familiar  with  it,  also  has  its  source  in  enormously  larger 
bodies  than  the  other  forces  with  which  we  are  familiar.  Lime 
binds  sandy  soils  and  loosens  compact  clay  soils.    It  is  an  important 


284  SOURCES  OF  EFFICIENCY 

source  of  agricultural  efficiency  to  take  advantage  of  these  two 
apparently  contradictory  properties. 

In  the  domain  of  living  organisms,  a  hybrid  plant  is  sometimes 
more  immune  to  disease  than  either  parent  species.  A  scratch  at 
one  time  may  be  barely  felt;  at  another  it  may  produce  death,  the 
action  in  the  first  being  additive,  in  the  latter  multiplicative.  The 
extract  from  the  thyroid  gland  in  the  human  body  is  necessary  to 
life,  yet  when  injected  directly  into  the  veins  it  kills  like  lightning. 
The  pancreatic  fluid  forms  sugar  in  the  intestine  and  destroys  it  in 
the  blood.  In  an  army  it  has  often  been  observed  that  some  frail 
looking  clerk  from  a  city  store  often  can  outmarch  a  husky  young 
giant  from  a  farm,  the  difference  being  due  to  the  fact  that  the 
nervous  energy  characteristic  of  the  former  type  of  physique  is  of  a 
higher  order  than  the  muscular  energy  prominent  in  the  latter. 

As  a  transition  from  the  biological  to  the  mental  field  we  may 
take  the  case  of  two  children  born  of  the  same  parents  but  differ- 
ing as  much  in  mental  capacity  as,  for  instance,  did  Joseph  and 
Napoleon  Bonaparte.  A  possible  explanation  is  that  in  the  one  child 
a  set  of  factors  may  act  together  in  an  additive  manner,  or  even 
cancel  each  other  in  a  measure ;  while  in  the  other  child  but  slightly 
different  factors  act  upon  each  other  in  multiplicative  and  progressive 
ways.  Cases  more  detailed  in  nature  are  the  fact  that  a  nerve  im- 
pulse will  travel  in  less  time  from  the  tip  of  the  finger  than  from 
the  elbow  to  the  brain ;  or  that  one  minute's  advice  from  an  expert 
at  a  cost  of  $100  is  cheaper  than  an  hour's  free  advice  from  an 
ignoramus. 

Error  in  More  Abstract  Fields 

One  of  the  most  important  forms  of  cognitive  error  is  that  of 
regarding  the  outside  appearance  as  corresponding  to  or  more  im- 
portant than,  the  inner  reality.  This  error  may  be  regarded  as 
essentially  a  mistake  with  reference  to  the  relation  of  the  upper 
and  lower  parts  of  an  order  of  materials  scale,  or  as  a  misuse  of 
symbolisms  with  respect  to  the  object  represented.  A  similar  case 
is  a  mistake  as  to  the  relations  of  words  and  the  actual  intention  of 
a  speaker,  or  any  distortion  of  the  meaning  of  any  act,  word,  or 
appearance.  Memory,  imagination,  and  reasoning  are  forms  of 
reuse  and  multiplicative  grouping,  hence  errors  in  them  are  essentially 
cases  of  misgrouping  of  some  kind.    Owing  to  their  abstract  nature 


ERROR  AND  PARADOX  285 

and  to  that  of  the  groups  involved,  efficiencies  of  high  order  are 
possible  in  their  treatment.  Mention  may  also  be  here  made  of  the 
paradox  that  the  more  one  knows,  the  less  one  knows.  The  study 
of  the  illusions  produced  by  a  sleight-of-hand  performer  or  so-called 
magician,  is  often  instructive  because  the  solution  of  a  trick  of  this 
kind  frequently  reveals  in  explicit  form  the  proximate  efficiental 
cause  of  the  error  involved.  Thus  some  of  these  illusions  are  due 
to  the  unrealized  fact  that  the  hand  of  the  performer  can  move 
more  rapidly  than  the  eye  can  follow,  or  to  a  failure  to  realize  the 
infinite  number  of  surfaces  that  go  to  make  up  a  solid  (as  in  the  flag 
trick),  or  to  appreciate  the  vast  number  of  externalities  which  may 
be  employed  in  such  performances  (as  externalities  above,  below, 
behind  the  stage,  or  in  other  persons),  or  the  limitations  in  the 
scope  of  one's  attentive  consciousness  (misgrouping).  So,  in  gen- 
eral, various  illusions  may  be  shown  to  be  due,  at  least  proximately, 
to  mis-efficientizing  of  some  sort,  and  this  knowledge  may  lead  to 
the  efficient  avoidance  or  correction  of  error,  often  with  many  dialec- 
tic results. 

Social  and  Religious  Errors 

By  a  cumulative  combination  of  the  preceding  sources  of  mistakes, 
as  well  as  for  independent  reasons,  history,  politics,  and  sociology 
are  full  of  errors  and  paradoxes.  Thus  the  greatest  political  crimes 
have  been  committed  in  the  name  of  liberty.  Civil  and  religious  wars 
have  been  the  most  bloody  and  cruel. 

Similarly  the  field  of  ethics  is  full  of  errors  of  the  most  vital  sort, 
the  dominant  cause  being  the  same  extreme  lack  of  externality. 
Examples  are  the  error  of  living  for  the  immediate  present,  and 
hence  in  prodigal  and  wasteful  fashion,  or  in  working  consciously 
or  unconsciously  for  narrow  selfish  ends.  Other  cases  are  the  fre- 
quent inconsistency  between  knowledge  and  action.  Still  other 
instances  are  the  errors  connected  with  the  paradoxical  fact  that 
intelligent  selfishness  leads  to  altruism. 

In  like  manner  the  whole  field  of  religion  and  theology  is  full  of 
error  due  to  misgrouping  of  the  vast  entities  involved.  Instances 
are  the  mistake  of  regarding  some  particular  type  of  infinite  extern- 
ality as  the  only  possible  one ;  or  of  regarding  some  special  method 
of  approaching  and  utilizing  infinite  externality  as  the  only  one 
allowable.    Also  each  form  of  conventional  religion  contains  princi- 


286  SOURCES  OF  EFFICIENCY 

pies  which,  in  certain  respects,  at  least,  are  paradoxical  and  the 
occasion  of  many  errors.  For  error  as  a  rule  is  proportional  to 
power,  and  "unexpected  sources  of  error  lurk  in  every  complicated 
process". 

When  errors  occur  primarily  with  reference  to  certain  categories, 
it  is  often  advantageous  to  characterize  and  group  them  with  respect 
to  these  categories,  even  though  the  various  instances  might  also  be 
classified  according  to  the  more  concrete  materials  in  which  they 
occur. 

Misconceptions  as  to  Dimensions 

Thus  among  the  groups  formed  with  reference  to  the  various 
categories  of  space,  are  errors  as  to  size,  form,  or  position.  Among 
the  most  subtle,  and  also  the  most  important  as  sources  of  waste  and 
hence  of  corrective  efficiency,  are  those  with  respect  to  dimensions. 
Thus  the  fact  that  it  is  harder  to  keep  money  than  to  make  it  is 
explained  by  the  fact  that  a  higher  dimension  of  time  is  involved  in 
the  former  case  than  in  the  latter.  A  machine  or  a  bridge  which  is  a 
success  in  the  model,  when  built  on  the  large  scale  demanded  by 
actual  practice  often  fails,  and  indeed  may  not  sustain  its  own  weight, 
the  error  involved  being  due  to  the  fact  that  the  weight  of  an  object 
increases  as  the  cube  of  its  linear  dimensions,  while  its  strength 
increases  only  as  the  square.  Lightning  strikes  at  a  single  point 
while  the  thunder  which  accompanies  it  is  heard  over  a  wide  area. 
The  unconscious  assumption  that  the  danger  from  lightning  extends 
over  the  area  throughout  which  the  sound  is  heard  is  the  source  of 
the  extreme  terror  often  produced  by  a  thunder  storm.  Similarly 
many  other  kinds  of  cowardice  may  be  cured  by  a  realization  of  the 
narrow  and  local  nature  of  the  evil  which  is  feared.  Likewise  it  is 
often  of  the  highest  importance  to  comprehend  the  fact  that  good  is 
higher  in  the  dimensions  of  its  efficiency  than  evil;  for  while  a 
method  of  doing  good  is  indefinitely  reusable  and  multiplicative,  any 
form  of  robbery  or  wrongdoing  can  be  repeated  only  a  few  times 
before  it  becomes  self -destructive. 

Some  Famous  Paradoxes  and  Errors  Explained 

To  complete  the  discussion  of  the  principle  in  hand,  it  may  be 
well  to  note  that  in  the  dimensional  principle  which  is  under  consider- 
ation, we  find  the  explanation  of  Pascal's  paradoxes  concerning  the 


ERROR  AND  PARADOX  287 

smallness  and  greatness  of  man.  For  man  is  small  in  his  additive 
relations  but  great  in  his  multipHcative  essence  and  powers.  A 
similar  explanation  holds  for  Kant's  antinomies;  for  the  universe, 
for  instance,  is  small  (or  finite)  when  the  multiplicative  principle  is 
used  to  condense  it,  and  large  (or  infinite)  when  the  same  principle 
is  used  to  expand  it.  A  special  application  of  the  fact  that  the 
world  is  small  owing  to  its  multiplicative  nature  is  found  in  the 
fact  that  a  traveller  in  any  given  place  on  the  earth,  usually  finds 
himself  near  some  acquaintance,  or  at  least  near  some  acquaintance 
of  an  acquaintance.  A  somewhat  different  application  is  the  fact 
that  when  processes  are  fully  understood  a  very  few  steps  will 
carry  us  from  the  data  of  common  life  to  their  most  abstruse  and 
technical  development.  An  example  is  the  way  in  which  gunpowder 
is  made  in  Jules  Verne's  Mysterious  Island,  by  a  shipwrecked  man 
deprived  of  the  ordinary  materials  supplied  by  civilized  life. 

Of  somewhat  similar  nature  are  errors  with  respect  to  the  ratio 
between  cause  and  effect,  or  in  the  various  proportions  of  objects. 
Illustrations  are  the  mistake  that  the  length  of  a  man's  jump  will  be 
in  proportion  to  the  length  of  his  running  start,  or  that  growth  and 
strength  will  correspond  to  the  amount  of  food  consumed.  Another 
important  error  of  this  class  is  a  disproportion  between  the  means 
employed  by  a  person  and  his  power  to  use  those  means. 

The  fallacy  of  the  undistributed  middle,  in  which  one  word  is 
unconsciously  used  in  two  or  different  senses,  is  an  example  of  error 
with  regard  to  number  and  symbols.  Illustrations  of  the  numerical 
paradoxes  which  are  frequently  connected  with  errors  are  the  state- 
ments that  the  greatest  things  are  both  simple  and  complex,  and  that 
the  universe  is  both  unitary  and  multitudinous. 

Temporal  Errors 

Besides  ordinary  errors  as  to  time,  we  have  its  paradoxical 
properties  such  as  are  implied  in  the  statements  that  life  is  short 
yet  long ;  that  all  things  are  old  yet  new.  Similarly  errors  occur  with 
respect  to  order.  These  often  take  extreme  resistant  forms,  while 
an  understanding  of  them  gives  a  deeper  grouping  of  the  facts  of 
life  with  new  and  higher  efficiencies  in  dealing  with  these  facts. 
Thus  in  the  history  of  the  human  race  we  find  that  contrary  to  the 
common  supposition  the  use  of  ornaments  such  as  bracelets,  neck- 
laces, and  rouge,  preceded  that  of  clothing,  and  that  animals  were 


288  SOURCES  OF  EFFICIENCY 

first  tamed  to  serve  as  pets  rather  than  to  serve  for  sources  of  food. 
This  is  an  illustration  of  the  fact  that  ideal  efficiency  is  more  primal 
than  concrete  utility.  What  was  originally  the  bottom  of  a  valley 
has  in  many  cases  become  a  mountain  top.  Similarly  v^e  have  a 
general  paradox  as  to  order  expressed  in  the  statement,  the  first 
shall  be  last  and  the  last  first. 

An  important  error  as  to  velocity  is  indicated  by  the  proverb 
"More  haste,  less  speed".  With  respect  to  quality,  we  have  that 
which  confuses  size  with  quality,  as  bigness  with  greatness. 

A  still  more  vital  and  inclusive  classification  of  cases  of  error  is 
obtained  by  grouping  these  according  to  the  various  Efficients  which 
are  primarily  misapprehended  or  misused  in  the  different  instances. 

Errors  as  to  Uniformities  and  Diversities 

In  particular  since  the  principles  of  uniformity  and  diversity  are 
of  primary  importance  in  making  groups  and  hence  in  forming  the 
other  Efficients,  the  correction  of  errors  in  regard  to  uniformity  and 
diversity  constitutes  a  conspicuous  method  of  obtaining  negative  and 
dialectic  efficiency.  For  instance  the  failure  to  realize  that  the 
surface  of  an  iron  rail,  though  apparently  smooth,  is  rough  enough 
to  have  great  frictional  properties,  hindered  the  early  development 
of  railroads.  For  in  the  absence  of  this  conception  engineers  thought 
that  the  rail  and  the  wheel  running  on  it  must  be  cogged  and  must 
operate  in  rack  and  pinion  fashion. 

Besides  such  common  violations  of  uniformity  as  inaccuracy  or 
want  of  certitude,  misconception  as  to  uniformities  often  take  the 
costly  form  frequently  denominated  **hasty  generalizations".  This 
consists  in  jumping  to  the  conclusion  that  what  is  true  of  certain 
members  of  a  class  is  true  of  all  members  of  the  class.  For  in- 
stance since  most  black  and  peaty  soils  are  fertile  some  farmers 
have  concluded  that  all  such  soils  are  rich  and  productive,  whereas 
such  soils  in  places  along  the  Mississippi  River,  for  example,  are  so 
deficient  in  potash  as  to  be  practically  barren. 

More  paradoxical  properties  of  uniformities  and  diversities  about 
which  errors  are  often  made  are  illustrated  by  the  fact  that  fre- 
quently the  greater  the  number  or  extent  of  a  uniformity  the  greater 
the  diversities  connected  with  it,  and  vice  versa.  The  latter  of 
these  cases  is  illustrated  by  the  properties  of  a  book,  which  is  essen- 


ERROR  AND  PARADOX  289 

tially  composed  of  separate  leaves,  as  compared  with  the  ancient 
manuscript  roll.  In  this  connection  may  also  be  mentioned 
Napoleon's  maxim,  that  nothing  is  so  certain  to  happen  as  the 
improbable. 

Errors  as  to  Groups 

A  hasty  generalization  may  also  be  regarded  as  a  group  made 
unduly  large.  In  like  manner  groups  may  be  made  too  small  or" 
otherwise  misused.  The  misuse  of  the  unit  and  multiplier  principle- 
is  illustrated  by  the  case  of  a  person  who  is  swindled  as  a  result  of 
taking  some  bait  that  has  been  held  out,  or  by  the  practice  on  the  part 
of  some  of  magnifying  the  errors  of  other  people  and  using  thera 
as  pretexts  and  handles  by  which  to  obtain  unworthy  advantages. 

Errors  in  regard  to  multiplicative  groups  are  of  many  kinds. 
Among  the  most  important  is  that  of  neglecting  or  failing  to  see 
the  importance  of  the  general  multiplicative  structure  of  a  domain. 
Examples  are  the  failure  to  realize  that  a  well  organized  team  of 
moderately  able  players  is  often  stronger  than  an  all  star  team  not  so 
well  organized ;  or  that  the  physical  texture  of  a  soil  is  more  impor- 
tant than  its  chemical  constituents.  Another  instance  is  that  of 
mistaking  a  case  of  tandem  for  one  of  parallel  elements  of  efficiency, 
or  vice  versa. 

Among  the  most  costly  errors  are  those  with  respect  to  the  rela- 
tive importance  of  factors  of  efficiency  in  a  given  multiplicative  or 
order  of  materials  scale.  Among  those  factors  which  are  often 
mistakenly  inverted  are  brain  and  brawn,  blessedness  and  happiness, 
quantity  and  quality.  An  error  of  this  kind  often  takes  the  form  of 
consuming  or  expending  the  framework  of  life  or  character,  as  if  it 
were  something  temporary  or  incidental. 

Errors  as  to  Externality 

Errors  in  regard  to  externality  are  of  great  importance.  Instances 
^re  egotism  and  selfishness  in  their  various  forms,  or  the  use  of  one 
method  of  obtaining  results  to  the  exclusion  of  other  methods.  In 
striving  for  results  it  is  of  especial  importance  to  remember  that 
what  is  efficiency  from  a  narrow  point  of  view  may  be  the  grossest 
waste  when  viewed  in  a  larger  way,  and  that  on  the  other  hand 
what  is  seeming  waste  may  be  real  economy  and  efficiency.  In  par- 
ticular efficiency  for  narrow  or  selfish  ends  in  the  long  run  is  not 


290  SOURCES  OF  EFFICIENCY 

efficiency  at  all,  but  relative  waste.  Similarly  as  a  rule  the  best 
and  quickest  route  to  extreme  technical  efficiency  lies  through  a 
manifold  grounding  in  fundamental  theoretical  principles.  Ex- 
pressed in  more  paradoxical  form  the  above  principle  becomes  pro- 
verbs like,  "Luxury  is  economy",  or  "The  longest  way  round  is  the 
shortest  way  home". 

Errors  as  to  Other  Efficients 

Errors  in  regard  to  symbols  are  numerous  and  often  vitally  im- 
portant because  of  the  wide  gap  which  usually  exists  between  an 
object  and  the  symbol  representing  it.  Such  errors  are  also  costly 
owing  to  the  highly  abstract  and  efficiental  nature  of  most  symbols. 
Both  of  these  causes  open  the  way  to  aggressive  and  wilful  abuses 
such  as  falsehood,  swindling,  and  forgery.  The  extreme  forms  which 
verbal  errors  may  take  are  illustrated  by  the  fact  that  an  entire 
legal  document  may  be  invalidated  by  the  omission  of  a  comma. 
Whole  classes  of  symbolic  errors  are  indicated  by  such  words  as 
misspelled,  misread,  misname,  miscalculate,  misrepresent,  and  other 
words  beginning  with  the  syllable  mis. 

A  great  variety  of  errors  also  appear  in  connection  with  the 
Efficient  which  we  have  termed  directive.  Large  classes  of  such 
errors  are  indicated  by  words  like  mistake,  misplace,  misdirect, 
misuse,  misapply,  misguide,  mismanage,  as  well  as  by  many  words 
formed  differently. 

Similarly  numerous  errors  occur  in  the  application  of  each  of 
the  other  Efficients.  These  may  take  general  forms,  such  as  the 
over  use  or  under  use  of  any  one  Efficient,  or  the  use  of  a  wrong 
species  or  of  a  faulty  combination  of  Efficients,  or  they  may  take 
more  individual  and  specific  forms.  Important  errors  which  relate 
to  all  processes  are  those  concerning  the  relative  values  of  the  re- 
sults of  different  processes. 

Forms  of  Errors 

Errors  may  also  be  classified  according  to  the  various  categories 
of  form.  Thus  important  cases  occur  which  may  be  characterized 
by  one  or  more  of  the  following  adjectives:  large,  small,  pervasive, 
cumulative,  conscious,  unconscious,  resultant,  manifold,  reciprocal, 
temporary,  permanent,  passive,  aggressive,  primary,  secondary, 
simple,  complex,  rhythmic.    An  example  of  a  resultant  error  is  one 


ERROR  AND  PARADOX  291 

composed  of  mistakes  as  to  the  size,  shape,  color,  and  duration  of 
any  object,  or  the  combination  of  errors  which  led  to  the  loss  of  the 
steamship  Titanic  in  April,  1912;  of  passive  errors,  are  those  due 
to  inertia,  or  imitation;  of  active  errors,  are  the  spendthrift  habit 
or  aggressive  wrongdoing  of  any  kind. 

Scales  of  Error 

Errors  high  in  a  multiplicative  scale  are  naturally  of  prime  impor- 
tance. An  error  may  be  of  high  order  either  because  it  occurs  with 
respect  to  some  material  of  high  order,  as  with  respect  to  some 
fundamental  principle  of  efficiency,  or  with  reference  to  any  Effi- 
cient. Also  an  error  which  leads  to  or  includes  a  number  of  other 
errors  is  of  high  order.  An  example  is  selfishness  or  wilful  ignor- 
ance about  the  laws  of  health.  A  like  place  is  held  by  an  error  with 
respect  to  the  nature  and  methods  of  correcting  errors. 

It  is  to  be  noted  in  this  connection  that  the  correction  of  any 
fundamental  mistake  includes  the  correction  of  a  host  of  subsidiary 
errors,  with  a  dialectic  of  other  useful  results. 

Transcendent  Errors 

Certain  errors  are  so  extreme  as  to  be  difficult  even  of  proximate 
explanation  and  hence  may  be  termed  transcendent.  The  tendency 
which  persons  feel  to  throw  themselves  from  the  top  of  a  precipice, 
and  to  which  an  individual  occasionally  yields  even  with  the  cer- 
tainty of  losing  his  life,  has  been  explained  as  due  to  the  fascina- 
tion produced  by  the  thought  "of  the  momentous  consequences  that 
would  result  from  such  a  comparatively  simple  act".  Nevertheless 
it  is  difficult  to  realize  how  disproportion  of  this  kind  could  work 
such  a  spell  that  a  person  would  sacrifice  his  life  in  order  to  have 
this  surplusage  experience.  Of  even  more  extreme  nature  however 
are  certain  cases  of  moral  wrongdoing  when  the  doer  is  fully  aware 
of  the  deadly  nature  of  the  results  of  evil  and  of  the  beneficial  out- 
come of  what  is  good. 

Paradoxes 

In  this  connection  special  mention  may  be  made  of  the  paradox. 
The  paradox  is  essentially  a  contradiction  between  outer  appearance 
and  inner  reality,  but  one  of  so  stubborn  a  nature  that  it  persists  in 
Ihe  mind  even  after  it  has  been  explained.    Illustrations  are  the  fact 


292  SOURCES  OF  EFFICIENCY 

that  in  winter  "as  the  days  begin  to  lengthen,  tlie  cold  begins  to 
strengthen";  or  the  ethical  principle  that  it  is  more  blessed  to  give 
than  to  receive;  or  the  spiritual  fact  that  he  would  gain  his  life 
must  lose  it.  These  paradoxes  are  all  capable  of  explanation  in 
terms  of  the  Efficients.  Thus  receiving  is  a  single  or  unitary  act, 
while  the  right  kind  of  giving  is  continuous  and  multiplicative  in 
nature,  and  hence  is  of  a  higher  order  of  efficiency;  hence  the  con- 
trast in  this  case  is  between  the  unit  and  the  multiple  or  product. 
Similarly  the  concrete  life  must  be  lost  in  order  that  the  abstract 
and  comprehensive  life  may  be  won,  an  application  being  thus  made 
of  principles  of  externality  and  orders  of  material. 

Similarly  the  human  will  is  measurably  free  in  the  field  of  the 
efficiency  abstract,  but  is  relatively  restrained  in  the  concrete  world. 
Nevertheless  owing  to  the  momentum  or  dynamic  of  certain  crude 
psychic  habits  the  feeling  of  contradiction  persists  to  some  extent 
ofter  the  explanation  has  been  made.  The  study  of  paradoxes 
however  is  often  particularly  useful  in  that  their  explanation  often 
brings  out  into  peculiarly  clear  light  the  essential  nature  of  many 
fundamental  errors  and  the  most  efficient  methods  of  preventing, 
correcting,  or  even  utilizing  these.  Such  a  study  also  by  remov- 
ing difficulties  opens  the  way  to  more  extensive  multiplicative  group- 
ings of  errors  than  would  otherwise  be  possible,  and  hence  to  greatly 
enlarged  efficiencies. 

Makers  of  Errors  Classified 

It  is  often  useful  to  classify  errors  according  to  the  agencies 
which  make  given  mistakes.    The  principal  classes  of  errators  are : 

( 1 )  Individual  persons,  or  certain  faculties  or  parts  of  a  personality 
such  as  the  memory  or  imagination. 

(2)  Small  groups  of  persons,  as  families. 

(3)  Societies  or  nations,  or  even  humanity  as  a  whole. 

It  will  be  noticed  that  the  number  of  agents  (that  is,  the  size 
of  the  acting  group)  involved  in  these  three  cases  increases 
progressively. 

Complex  Errors 

The  different  species  of  error  and  paradox  which  have  been  men- 
tioned in  the  preceding  pages  may  be  combined  in  various  ways. 
A  number  of  illustrations  of  complex  mistakes  have  already  been 


ERROR  AND  PARADOX  293 

given,  but  a  still  more  complex  case  is  found  in  the  various  errors 
which  have  acted  as  a  continuous  and  often  cumulative  stream  in 
human  history,  and  which  together  with  other  limitations  have  held 
human  efficiency  in  so  many  respects  within  narrow  limits. 

An  illustration  of  paradox  combined  with  error  is  the  fact  that 
Faraday,  although  he  discovered  the  principle  of  the  dynamo,  classed 
the  electro-magnetic  engine  with  mesmerism  and  perpetual  motion, 
and  called  them  all  "ill  weeds  which  cannot  be  extirpated".  A 
similar  instance  is  the  fact  that  Charles  Darwin  was  publicly  repri- 
manded in  the  Shrewsbury  school  for  setting  up  a  laboratory  for 
scientific  experiment. 

These  instances  illustrate  both  the  great  difficulty  in  detecting  and 
preventing  complex  or  compound  errors,  and  also  the  large  efficiency 
results  which  may  often  be  obtained  by  so  doing. 

NATURE   AND    EFFICIENCY    RELATIONS   OF    ERROR 

The  nature  and  sources  of  error,  or  at  least  the  best  way  of  regard- 
ing these  matters  for  efficiency  purposes,  have  of  necessity  been 
indicated  in  large  measure  in  the  part  of  the  chapter  which  pre- 
cedes. It  will  be  useful  however  to  state  some  of  these  properties 
more  systematically  and  to  call  attention  to  certain  additional  ones. 

Dual  Nature  of  Error 

Every  case  of  error  may  be  regarded  as  dual  in  nature;  that  is, 
as  containing 

( 1 )  a  more  or  less  ultimate  element,  viz. :  the  fundamental  prin- 
ciple of  limitation  acting  through  personality; 

(2)  a  relative  or  approximate  element,  viz. :  that  of  the  misuse 
in  some  way  of  an  Efficient  or  of  a  combination  of  Efficients.  The 
useful  properties  connected  with  the  first  of  these  elements  have 
been  stated  in  the  preceding  chapter  and  need  not  here  be  repeated. 

Multiplicative  Element  in  Error 

With  respect  to  the  second  of  these  two  elements,  the  realization 
of  error  as  due  to,  or  at  least  accompanied  by,  the  multiplicative 
principle  facilitates  an  appreciation  of  the  enormous  number  of 
ways  in  which  error  may  arise,  and  of  the  explosively  destructive 
consequences  of  many  mistakes ;  aids  in  the  recognition  and  admis- 
sion of  one's  own  mistakes,  and  in  the  treatment  of  those  of  others, 
charitably  and  in  other  efficient  ways. 


294  SOURCES  OF  EFFICIENCY 

Advantages  in  Efficiental  View  of  Error 

Thus,  for  example,  the  above  conception  makes  clear  in  striking  yet 
safe  ways  that  what  is  often  regarded  as  pure  folly  or  malice  may 
contain  much  that  is  good  and  usable.  As  has  been  remarked  in 
another  connection,  the  dominant  motive  in  a  bullying  schoolboy  is 
pleasure  in  the  exercise  of  his  directive  faculty,  the  nature  of  the 
effect  on  others  being  entirely  secondary.  The  use  of  these  powers 
may  frequently  be  freed  from  error  and  directed  into  useful  channels. 
The  same  analysis  applies  to  many  of  the  tyrannies  and  other  errors 
of  older  persons.  Or,  in  general,  the  efficiental  view  of  error  and 
wrongdoing  often  separates  and  sets  free  certain  Efficients  and 
allows  and  stimulates  them  to  act  aggressively  and  effectively. 

In  this  connection  it  is  well  to  note  that  error  is  often  in  proportion 
to  power ;  that  it  is  the  man  of  energy  and  constructive  capacity  who 
makes  mistakes.  In  other  words,  where  there  is  much  waste  there  is 
much  to  save  and  utilize. 

The  above  multiplicative  view  of  error  also  makes  clear  the  need 
and  value  of  treating  error  by  manifold  checks  and  tests  and  by 
inclusive  group  methods.  It  also  indicates  the  rich  dialectic  results 
which  are  likely  to  follow  such  methods  of  treatment,  and  stimulates 
one  to  apply  such  processes. 

Advantageous  Use  of  Error  and  Waste 

As  has  been  stated  in  another  place,  in  certain  circumstances, 
especially  when  hemmed  in  by  certain  limitations  which  for  the 
present  seem  insuperable,  the  elimination  of  waste  is  the  most 
available  source  of  additional  efficiency.  Often  also  error  and 
waste  are  the  most  conspicuous  signs  of  possible  new  positive 
efficiencies,  and  the  most  manageable  routes  by  which  to  attain 
these.  Also  in  competitive  work  a  large  element  of  success  consists 
in  merely  taking  advantage  of  the  mistakes  of  others.  Napoleon 
Bonaparte,  for  example,  obtained  many  of  his  greatest  victories  in 
this  way.  This  method  of  procedure  in  obtaining  efficiency  is  entirely 
legitimate  when  the  mistakes  of  evildoers  are  utilized  as  a  means  of 
overthrowing  such  people,  or  the  errors  of  any  class  of  persons  are 
employed  as  a  means  of  benefiting  them.  The  mistakes  made  by 
other  people  may  often  also  without  impropriety  be  regarded  as 
experiments  made  for  our  benefit  without  cost  to  us. 

Similarly  if  the  multiplicative  elements  which  are  in  conflict  in  a 


ERROR  AND  PARADOX  295 

paradox  be  realized,  by  this  very  means  these  elements  are  set  free 
to  act  independently,  yet  in  a  certain  measure  with  mutual  helpful- 
ness since  they  stimulate  each  other  to  develop  in  different  fields  while 
still  maintaining  useful  relations.  The  efficiental  explanation  of 
paradoxes  also,  as  has  been  remarked,  clears  the  field  of  obstacles  and 
thus  opens  the  way  to  deeper  unities  and  freer  action. 

Era  of  Progress  often  preceded  by  Period  of  Error 

After  the  above  study  of  the  relation  of  error  and  paradox  to 
efficiency,  it  is  not  surprising  to  find  that  almost  every  important 
epoch  of  human  progress  has  been  preceded  by  a  stage  of  error  and 
need,  the  more  or  less  efiiciental  treatment  of  which  has  led  to  the 
subsequent  period  of  progress.  Thus  we  have  the  age  of  the 
Sophists  before  Socrates,  and  the  period  of  decadent  Greek  and 
Roman  morality  before  Christ.  Similarly  the  destructive  Hume 
preceded  the  constructive  Kant.  At  various  times  eras  of  political 
oppression  have  been  followed  by  periods  of  freedom  and  progress. 
The  principal  ways  in  which  error  and  evil  tend  to  produce  reaction 
and  new  efficiencies  have  been  indicated  in  the  preceding  pages. 

METHODS  OF  EFFICIENT  TREATMENT 

Many  principles  and  details  with  respect  to  the  most  efficient 
methods  of  treating  error  are  contained  in,  or  follow  obviously  from 
the  preceding  discussion.  It  will  be  useful  however  to  make  certain 
additional  statements  as  to  this  matter  and  to  present  the  whole  topic 
in  a  more  systematic  form. 

Multiplicative  Principle  an  Aid  in  Various  Ways 

The  multiplicative  principle  not  only  aids  us  in  realizing  the  great 
number  of  ways  in  which  errors  may  arise,  but  also  the  extreme  forms 
which  errors  and  their  consequences  may  take.  Hence  it  also  sug- 
gests the  importance  of  using  wherever  possible  a  variety  of  checks 
and  cross  multiplicative  groupings  in  preventing,  correcting,  or  utili- 
zing errors  in  a  given  domain  of  material;  and  it  also  makes  clear 
the  numerous  tests  which  are  usually  available.  Examples  of  checks 
in  the  forms  of  cross  multiplicative  groups  are  the  double  entry  in 
bookkeeping  and  the  initiative  and  referendum  in  government. 

One  of  the  methods  by  which  the  proprietor  of  a  large  business 
often  secures  efficiency  in  its  management,  is  that  of  dividing  the 


296  SOURCES  OF  EFFICIENCY 

business  into  sections  or  departments,  and  requiring  daily  reports  of 
the  cost  and  profit  of  each  department.  Any  waste  or  error  in  any 
one  section  is  thus  quickly  revealed  and  remedied.  This  constitutes 
a  highly  important  application  of  the  group  method  in  the  treatment 
of  error,  and  one  which  frequently  gives  rise  to  new,  aggressive, 
and  often  dialectical  efficiencies. 

Application  of  Principle  of  Diversity 

The  principle  of  diversity  is  often  a  valuable  auxiliary  in  this 
connection.  Thus  if  a  page  of  proof  be  corrected  first  entirely  with 
respect  to  the  spelling,  then  with  respect  to  the  punctuation,  and  so  on 
for  other  individual  elements,  a  more  thorough  correction  and  utili- 
zation of  error  will  be  obtained  than  if  all  the  sources  of  error  be 
treated  simultaneously. 

Manifold  Treatment  of  Highest  Material 

This  multiplicity  of  safeguards  is  of  especial  importance  with 
respect  to  material  which  in  any  given  case  stands  highest  in  the 
scale  of  importance.  Thus  the  traveller  should  frequently  check  up 
his  money  and  at  all  times  should  vigilantly  protect  it  from  loss  or 
error.  So  the  wide  awake  business  man  carefully  notes  the  char- 
acter of  each  document  to  which  he  affixes  his  signature.  Every  wise 
man  in  like  manner  will  jealously  guard  certain  first  principles  of 
life  and  action  to  see  that  they  are  not  impaired  or  encroached  upon. 

Similarly,  cases  of  especially  difficult  error,  persistent  fallacies, 
paradoxes,  and  mysteries  call  for  the  use  of  extreme  and  manifold 
externality  and  cross  treatment.  With  sufficient  externality  a  clue 
to  each  tangle  usually  somewhere  comes  to  the  surface. 

Application  of  Unit  and  Multiplier 

The  unit  and  multiplier  principle  is  often  of  great  service  in  the 
treatment  of  error.  For  instance  its  use  often  prevents  the  exag- 
geration of  a  difficulty  and  the  dismay,  discouragement,  and  other  evil 
results  which  would  follow.  When  applied  in  the  form  of  experiment 
it  frequently  is  a  means  of  avoiding  loss  of  time  and  resources,  and 
sometimes,  either  directly  or  indirectly,  leads  to  the  solution  of  a 
difficulty.  In  cases  of  doubt  the  erroneous  nature  of  a  principle  may 
often  be  detected  by  developing  the  consequences  of  such  a  principle 
by  the  unit  and  multiplier  method.    When  used  in  the  step  by  step 


ERROR  AND  PARADOX  297 

form  of  the  Greek  logic,  this  method  often  prevents  or  corrects 
theoretic  errors,  or  unravels  abstract  difficulties.  When  utilized  as 
a  means  of  realizing  the  consequences  of  an  act  or  principle,  it 
serves  to  arouse  the  attention  and  to  stimulate  to  action  in  safe- 
guarding against  mistakes. 

Application  of  Other  Efficients 

The  principle  of  reuse  may  also  be  of  service  in  this  connection. 
An  instance  is  the  reuse  which  one  makes  of  the  experience  of  others 
in  the  matter  of  mistakes  and  difficulties.  A  person  utilizes  this 
principle  when  consulting  a  specialist  in  a  given  line. 

It  is  often  important  to  remember  that  it  does  not  pay  to  try  to 
prevent  all  error  and  waste  from  this  source,  but  rather  that  it  is 
frequently  best  to  proceed  by  the  most  available  efficiency  methods 
and  from  time  to  time  to  correct  as  far  as  possible  such  errors,  and 
provide  for  such  wastes  as  may  have  arisen.  Similarly  it  may  be 
advisable  at  times  to  allow  the  results  of  the  errors  of  others  to  accu- 
mulate till  in  time  they,  in  a  measure,  check  themselves.  This  in 
effect  constituties  a  use  of  the  rhythmic  method  in  the  backeddy  and 
often  dialectic  form. 

In  another  aspect  this  method  consists  of  giving  the  leading  place  to 
the  creation  of  aggressive  efficiency,  and  a  secondary  place  to  the 
prevention  of  all  errors.  It  pays  better  to  try  to  have  a  large  surplus 
on  hand  with  which  to  pay  for  some  errors,  rather  than  to  try  to 
avoid  all  mistakes.  This  is  especially  true  in  the  more  inventive  and 
creative  elements  of  life  and  action. 

Study  of  Special  Pitfalls 

It  is  well  to  remember  also  that  each  special  field  of  work  or 
life  has  its  own  particular  pitfalls  or  characteristic  sources  of  error 
and  consequent  waste.  Hence  it  is  important  carefully  to  study  the 
mistakes  which  are  made,  or  are  likely  to  be  made,  in  any 
given  domain;  to  ascertain  their  sources  as  far  as  possible;  and  to 
treat  them  in  systematic  ways.  At  this  point  is  evident  the  value 
of  as  complete  a  knowledge  as  possible  of  the  facts  and  principles  of 
the  various  branches  of  science.  Similarly  it  behooves  each  person 
to  make  a  study  of  the  mistakes  which  are  characteristic  of  his  per- 
sonality, and  which  therefore  he  is  most  likely  to  make. 


298  SOURCES  OF  EFFICIENCY 

Other  General  Principles  for  Treatment  of  Error 

In  the  treatment  of  paradoxes  it  is  desirable  to  keep  in  mind  the 
fact  that  some  powerful  source  of  efficiency  is  usually  close  to,  or  is 
contained  in,  each  apparent  contradiction  of  this  kind ;  and  that  it  is 
important  to  use  as  extensively  as  possible  each  source  of  efficiency 
involved  in  such  contradictions,  no  matter  how  opposed  to  each  other 
some  of  these  sources  may  seem  to  be  at  times.  Thus  the  fact  that 
lime  when  applied  to  soils  both  binds  a  loose  soil  and  loosens  a 
compact  one  shows  the  wide  and  manifold  value  of  this  chemical 
element  in  agriculture. 

In  all  cases  the  power  of  externality  to  convert  a  mistake  into  a 
source  of  ultimate  advantage  is  to  be  noted.  In  fact  it  is  not  too 
extreme  a  statement  to  say  that,  with  few  exceptions,  no  matter  what 
error  one  commits,  if  one  has  or  acquires  large  enough  externality 
one  may  convert  such  error  into  something  advantageous.  In  the 
rhythmic  series  involved  all  depends  on  the  degree  of  ultimate 
externality. 

In  general  it  is  important  to  remember  that  the  entire  body  of  the 
Efficients  is  the  most  effective  agent  available,  both  in  detecting 
errors  and  in  treating  them  in  the  most  useful  way. 

Synopsis  of  Chapter 

An  especially  important  form  of  limitation  is  the  active,  personal 
one  termed  error.  The  peculiar  gravity  of  this  species  of  limitation 
arises  from  the  fundamental  place  and  function  of  personality  in 
all  efficiency  processes.  Also  the  correction  of  error  and  removal 
of  waste  often  form  a  peculiarly  easy  way  of  improving  a  process. 
Errors  may  be  conveniently  classified  according  to  the  objects  to 
which  they  relate,  according  to  the  personalities  making  mistakes, 
or  with  respect  to  the  forms  which  errors  assume.  Of  prime  im- 
portance are  those  in  regard  to  the  fundamental  qualities  of  objects, 
to  spatial  dimensions,  to  uniformities  and  diversities,  to  groups  or 
other  Efficients.  A  paradox  is  an  error  which  persistently  recurs 
after  it  has  been  explained. 

It  is  of  the  first  importance  to  realize  that  every  error  contains 
both  an  ultimate  and  an  approximate  or  contingent  element,  and 
that  the  latter  of  these  consists  essentially  in  some  mistake  with 
reference  to  the  multiplicative  principle,  and  more  particularly  with 
reference  to  one  or  more  of  the  Efficients.    Often  by  realizing  errors 


ERROR  AND  PARADOX  299 

in  this  way  they  may  be  avoided  or  corrected  in  large  groups. 
Hence,  in  general,  the  best  way  to  avoid,  correct,  and,  in  some 
cases,  to  utilize  errors  is  by  a  thorough  study  and  careful  appli- 
cation of  the  multiplicative  principle  in  its  various  forms. 


EXERCISE  18 

1.  State  and  explain  some  costly  mistake  due  to  a  misunderstanding  of 
the  dimensions  involved  in  the  material  considered.     (See  p.  286.) 

2.  Give  two  instances  of  hasty  generalizations  with  disastrous  conse- 
quences.   Show  how  these  errors  might  have  been  avoided  by  efficiental  means. 

Give  an  example  of 

3.  A  fallacy  5.  An  idol  of  the  tribe 

4.  An  idol  of  the  den  6.  An  idol  of  the  forum 

7.  Of  the  other  principal  kinds  of  error, 

8.  At  an  expenditure  of  $300,000  a  city  so  diminished  the  leaks  and  wastes 
in  its  water  system  that  an  expenditure  of  $3,600,000  in  order  to  increase  its 
water  supply  was  avoided.  State  the  degree  of  efficiency  involved.  Describe 
possible  dialectic  efficiencies  which  might  follow. 

9.  Give  an  lillustration  of  your  own  of  increased  efficiency  obtained  by  the 
elimination  of  waste  instead  of  by  an  enlargement  of  plant. 

10.  If  in  a  given  country  the  annual  loss  from  forest  fires  is  $50,000,000 
and  an  annual  expenditure  of  $5,000,000  will  prevent  half  of  this  loss,  state 
the  degree  of  efficiency  of  the  expenditure, 

11.  Give  an  instance  of  your  own  where  the  correction  (or  prevention) 
of  an  error  has  had  dialectic  efficiency  results. 

Explain  each  of  the  following  paradoxes : 

12.  Hot  and  cold  applications  to  a  part  of  the  human  body  often  produce  the 
same  effect, 

13.  Genius  and  insanity  are  closely  related. 

14.  At  the  seashore,  the  hotter  the  sun's  rays  the  cooler  the  sea  breeze, 

15.  A  cool  sea  breeze  means  warm  surf  bathing. 

16.  Give  an  error  that  is  dual  17.  Manifold  18.  Of  high  order 

19.  State  the  species  of  error  implied  in  the  statement  "all  is  not  gold  that 
glitters". 

20.  Give  two  examples  of  optical  illusions  with  explanations  of  the  same. 
Show  how  these  explanations  may  be  made  the  basis  of  aggressive  efficiencies. 

21.  How  is  it  possible  that  some  rivers  at  certain  seasons  of  the  year  flow 
up  stream? 

22.  Why  should  the  river  Nile  be  smaller  near  its  mouth? 

23.  Why  is  it  that  that  which  looks  most  easy  to  do,  as  the  playing  of  a 
violin  by  an  expert,  is  often  most  difficult? 

24.  Give  two  examples  of  paradoxes  with  explanations  of  the  same  in 
terms  of  the  principles  of  this  book. 

How  might  these  explanations  be  made  sources  of  efficiency? 


300  SOURCES  OF  EFFICIENCY 

25.  Why  is  it  that,  in  some  respects,  the  best  way  to  see  the  country  is  to 
go  to  the  city? 

26.  Give  an  example  of  an  error  arising  from  confusing  quantity  with 
quahty. 

27.  Why  is  it  that  many  persons  think  of  Palestine  as  larger  than  New- 
foundland or  Peru? 

28.  Give  an  example  of  a  mistake  due  to  inertia  or  momentum. 

29.  State  and  explain  the  principles  of  efficiency  involved  in  the  statement 
that  the  serpent,  though  it  has  no  limbs  can  "outclimb  the  monkey,  outswim 
the  fish,  outleap  the  jerboa,  and,  suddenly  loosening  the  coils  of  its  crouching 
spiral,  it  can  spring  into  the  air  and  seize  the  bird  on  the  wing". 

30.  Why  is  it  that  a  person  is  often  the  most  solitary  when  in  a  crowd? 

31.  Give  an  example  of  an  error  which  consists  essentially  of  regarding  a 
multiplicative  process  or  relation  as  merely  additive? 

32.  Give  an  instance  where,  instead  of  trying  to  prevent  all  error  and  waste 
greater  net  efficiency  is  obtained  by  employing  in  aggressive  ways  the  energy 
that  would  be  thus  spent.  In  this  connection  what  is  the  meaning  of  the 
business  man's  profit  and  loss  account? 

Give  an  instance 

SS.  Where  the  use  of  externality  has  been  the  means  of  detecting  error 
or  loss. 

34.  Where  the  use  of  externality  has  prevented  error  or  waste. 

35.  Where  the  use  of  cross  multiplicative  groups  detects  or  prevents  error. 

36.  Where  the  use  of  the  unit  and  multiplier  principle  has  prevented  waste. 

37.  Why  are  the  simplest  things  often  the  hardest  to  understand? 

38.  What  efficiental  term  would  be  used  in  describing  an  error  concerning 
errors  ? 


CHAPTER  XVII 

COMBINATIONS  OF  EFFICIENTS 
SUMMARY 

Illustrations  of  Combinations  of  Efficients 

When  man  supports  himself  by  hunting  and  fishing,  he  uses 
food  which  is  of  a  high  nutritive  value,  but  one  which  is  relatively 
scarce.  Hence  in  the  hunting  and  fishing  stage  of  civilization  man 
necessarily  lived  in  a  somewhat  isolated  manner.  When  men  who 
have  tried  to  support  themselves  in  this  way  have  multiplied  in 
numbers,  it  has  become  necessary  for  them,  in  the  end,  to  subsist 
more  and  more  on  vegetable  products.  Such  food  is  of  a  relatively 
low  order,  but  it  has  the  property  that  by  externality  and  by  the 
cooperation  of  the  producers  it  may  be  made  very  abundant.  Hence 
its  preparation  in  time  came  to  be  accompanied  by  an  elaborate 
social  organization  with  many  unexpected  resultant  advantages  such 
as  a  high  degree  of  mental  development  and  of  the  arts  and  sciences 
which  accompany  such  development.  The  complex  social  organiza- 
tion of  certain  kinds  of  insects,  as  of  some  species  of  ants,  and  their 
great  relative  intelligence  find  a  like  explanation.  Originally  ants 
were  meat  eaters  and  like  spiders  lived  approximately  solitary  lives. 
The  stages  may  be  traced  by  which,  as  their  food  changed,  first  to 
the  mixed  form  and  then  to  a  vegetable  basis,  their  social  organiza- 
tion and  general  intelligence  also  developed.  These  cases  are  illus- 
trations of  the  fact  that  in  a  world  full  of  diversity,  limitation,  and 
active  competition,  more  effective  results  are  obtained  by  using  a 
combination  of  efficiency  agencies  than  by  the  use  of  any  single  one. 

General  Statement  of  Advantages 

In  general  the  employment  of  a  combination  of  the  primal  instru- 
ments of  efficiency,  instead  of  one  only,  usually  makes  possible  a 
closer  contact  with  the  actualities  of  the  world  of  fact  than  is 
otherwise  possible.  Hence  result  certain  intense,  and  often  sudden 
and  dynamic  efficiency  results  which  are  of  the  highest  importance 
in  a  world  of  competition.     Various  efficiency  methods  when  com- 

'01 


302 


SOURCES  OF  EFFICIENCY 


bined  in  a  given  process  often  interact  also  in  ways  so  manifold 
and  complex  as  to  be  impossible  to  trace  in  detail. 

For  instance,  in  the  rotation  of  crops  in  agriculture  we  evidently 
have  a  use  of  the  principles  of  diversity,  directive,  and  rhythm. 
But  these  result  in  other  efficiency  principles  such  as  the  retention 
and  reuse  of  farm  laborers  the  year  round,  the  greater  reuse  of  farm 
machinery,  utilization  of  by-products,  the  prevention  of  waste  as 
by  the  destruction  of  insect  pests,  a  uniformity  of  returns,  and 
many  other  useful  results  and  agencies. 

Similarly  in  various  forms  of  business,  in  education,  in  govern- 
ment, and  in  almost  all  actual,  fruitful  processes,  we  find  a  combina- 
tion of  efficiency  agencies  at  work.  Often  by  careful  study  such 
combinations  may  be  developed  to  a  far  higher  degree  of  efficiency. 

Apart  from  their  so-called  business  or  practical  uses,  various 
bizarre  combinations  of  efficiency  agencies  prevent  work  from  de- 
generating into  a  mere  formalism,  and  go  far  to  give  spice,  variety, 
and  charm  to  life. 

Classes  of  Combinations 

Evidently  the  possible  forms  and  species  of  combinations  of  Effi- 
cients is  without  limit  in  form  and  number.  In  the  preceding  chap- 
ters the  different  forms  which  each  Efficient  may  assume  have  been 
outlined,  and  plainly  the  number  of  different  combinations  that  may 
be  made  of  these  various  species  vastly  exceed  the  varieties  of  any 
one  agent.  A  realization  of  some  of  the  principal  forms  of  com- 
binations will  be  an  aid  in  selecting  the  best  combination  for  use 
in  any  given  case,  and  will  be  useful  in  many  other  ways. 

Loose  Combinations  of  Efficients 

In  the  first  place  we  have  those  combinations  of  Efficients  which 
are  comparatively  loose  and  incoherent.  A  situation  may  be  so 
difficult  that  in  it,  especially  at  first,  it  is  possible  to  use  only  what 
may  be  termed  efficiental  opportunism;  that  is,  to  employ  such  local 
and  fragmentary  efficiency  methods  as  may  be  available  from  time 
to  time  and  to  leave  the  rest  to  future  development.  Simple  in- 
stances of  this  process  are  that  of  looking  at  a  subject  from 
various  points  of  view,  or  of  working  at  a  problem  along  various 
lines.  So  in  business  greater  efficiency  is  obtained  by  applying 
adapted  methods  of  obtaining  results,  to  buying,  manufacturing. 


COMBINATIONS   OF  EFFICIENTS  303 

selling,  and  accounting  than  could  be  obtained  by  trying  to  develop 
.all  of  these  by  one  exclusive  procrustean  method. 

The  more  abstract  cases  of  this  general  type  of  combination  are 
illustrated  by  the  advantages  in  combining  and  using  different  views 
of  electricity,  no  matter  how  contradictory  these  theories  may  appear 
from  some  points  of  view.  For  if  electricity  be  regarded  in  cer- 
tain cases  as  composed  of  small  units  called  electrons;  in  other 
cases,  as  a  combination  of  positive  and  negative  fluids ;  and  in 
still  others,  as  stresses  or  undulations  in  the  ether,  it  is  found  that 
better  results  are  obtained  in  the  aggregate,  than  if  any  one  of  these 
seemingly  opposed  views  were  used  alone. 

An  important  instance  of  somewhat  different  nature  is  that  of 
organizing  a  business  or  a  nation  in  such  a  way  that  it  shall  be  char- 
acterized at  the  same  time  by  the  utmost  system  (or  multiplicative 
group  organization)  and  also  by  the  greatest  possible  freedom 
(diversity)  and  initiative  (directive)  on  the  part  of  the  individuals 
and  other  units  composing  it. 

Often  it  is  well  (or  even  necessary)  for  a  time  to  develop  each 
strand  or  element  of  efficiency  in  a  given  situation,  with  little  or 
no  regard  to  the  other  sources  or  strands,  and  to  wait  or  work  for 
later,  more  definite  combinations  and  crystallizations. 

As  a  transition  to  the  next  general  class  of  combinations  mention 
may  be  made  of  the  conscious  formation  of  habits  as  a  source  of 
efficiency.  This  involves  the  combined  use  of  the  following  effi- 
cients:  reuse  both  objective  and  subjective,  specialism  (or  diversity) 
and  uniformity  in  kinds  of  activity,  externality  in  the  shape  of  extra 
educational  practice,  a  resulting  speed  and  force  of  action,  and  the 
substitution  of  lower  for  higher  and  more  costly  energy. 

Close  Combinations  of  Efficients 

Another  important  form  of  combinations  of  efficiency  agents  is 
that  in  which  the  component  agents  are  so  closely  knit  together  that 
their  individuality  is  largely  lost  in  that  of  the  whole.  Thus  the 
efficiency  of  the  human  body  arises  to  a  great  extent  from  the  fact 
that  the  various  agents  and  sources  of  effectiveness  in  it  are  in 
many  places  and  respects  so  completely  fused  together.  We  here 
find,  for  example,  various  uniformities  and  diversities  among  the 
cells,  tissues  and  organs;  multiplicative  groups  of  many  species, 
both  articulate  and  constitutive ;  orders  of  materials,  as  illustrated  by 
the  series,  brain,  nerve,  flesh,  bone;  externality  operating  through 


304  SOURCES  OF  EFFICIENCY 

the  eye  and  hand,  and  many  subjective  reciprocal  externaHties ; 
varied  reuse  of  each  organ ;  and  symbolisms,  force,  motion,  directive^ 
rhythms,  and  dialectics  of  various  kinds.  But  the  whole  aggre- 
gate is  so  closely  knit  together  as  to  form  a  solid  contexture  of 
efficientisms;  in  fact  a  unity  is  present  which  is  perhaps  beyond 
analysis.  This  fact  is  the  source  of  efficiency  results  which  are  far 
beyond  those  which  could  be  obtained  from  the  agents  specified  in 
the  above  list  if  used  in  scattered  fashion.  The  same  principle  holds 
in  even  higher  degree  of  the  human  mind.  The  efficiency  relations 
involved  in  a  thoroughly  united  human  family  are  of  like  nature. 

Many  of  the  sources  of  success,  that  is,  methods  of  obtaining  re- 
sults, as  popularly  stated,  are  of  this  mixed  and  closely  fused  nature. 
Illustrations  are  the  terms  shrewdness,  good  health,  magnetism, 
native  ability,  or  even  genius.  Thus  shrewdness  includes  power  to 
perceive  differences  (or  diversities)  where  other  persons  see  only 
uniformity;  to  look  beyond  the  immediate  present  (externality); 
to  penetrate  beneath  the  surface  of  things  (use  of  orders  of  ma- 
terial) ;  and  the  avoidance  of  error.  Any  highly  developed  or 
thoroughly  mastered  art  of  doing  things,  as  contrasted  with  the 
science  or  knowledge  of  them  is  largely  a  thoroughly  fused  com- 
bination of  efficiency  processes  of  the  general  type  under  discussion. 
Instances  in  another  field  are  the  concepts  of  harmon)^,  beauty,  and 
sublimity.  Thus  many  mechanical  and  formal  rules  are  combined  in 
a  statue  like  the  Venus  of  Milo,  but  they  are  so  completely  com- 
bined, or  interact  so  subtly,  that  their  complete  analysis  is  impossible. 

In  an  even  more  abstract  world,  it  may  be  shown  that  concepts 
like  those  of  space,  time,  and  cause  are  instruments  of  the  highest 
efficiency,  and  that  this  efficiency  is  greatly  increased  if,  in  certain 
respects,  each  of  them  be  regarded  as  a  closely  knit  aggregate 
of  primal  Efficients. 

Combinations  built  up  progressively 

Systems  of  Efficients  which  have  been  built  up  progressively  in 
time,  or  are  the  result  of  a  species  of  growth,  even  though  these 
systems  contain  elements  which  are  in  large  part  mere  survivals  by 
virtue  of  inertia,  are  often  peculiarly  rich  and  effective.  An  example 
is  the  English  form  of  government.  The  human  body  and  human 
mind  as  described  above,  and  most  of  the  general  concepts  in  use 
are  of  the  same  general  nature.  >> 


COMBINATIONS   OF  EFFICIENTS  305 

Mottled  Combinations  of  Efficients 

As  a  result  of  human  directive  action  and  of  processes  of  natural 
development,  many  combinations  are  of  a  varied  or  mottled  char- 
acter with  respect  to  the  closeness  with  which  their  components 
are  aggregated.  Thus  in  some  parts  of  any  highly  developed  busi- 
ness the  Efficients  are  loosely  aggregated  and  in  others  they  are 
highly  fused.  The  same  will  be  found  to  be  true  of  almost  all 
efficiency  processes  in  actual  operation  in  the  concrete  world  if  thor- 
oughly examined.  In  many  cases  this  diversity  is  the  result  of  what 
seems  caprice  or  even  error,  in  others  it  means  a  closer  adaptation  to 
limitations  and  qualities  beyond  control,  and  hence  is  a  source  of 
important  added  efficiency. 

The  above  considerations  suggest*  certain  remarks  as  to  the  best 
methods  of  using  combinations  of  Efficients  in  actual  practice.  In 
the  first  place  it  may  be  noted  that  such  combinations  in  some  cases 
form  a  crude,  initial  instrument  by  which  to  attack  a  problem  or 
treat  a  situation ;  but  that  in  other  cases  they  form  a  highly  finished, 
final  instrument;  and  that  they  may  have  every  degree  of  develop- 
ment and  value  between  these  extremes. 

Efficient  Transitions 

Again  in  order  to  obtain  results  of  the  highest  order  from  the 
use  of  groups  of  Efficients,  especially  of  the  more  developed 
combinations,  it  is  often  important  to  make  the  transition  from  one 
component  in  them  to  another  with  a  certain  deft  and  invisible 
swiftness.  The  changes  in  the  moods  and  methods  of  an  accom- 
plished orator  illustrate  this.  Frequently  added  efficiency  is  ob- 
tained by  the  concentration  of  some  one  or  more  of  the  involved 
Efficients  into  a  momentary  intensity.  This  principle  also  is  illus- 
trated by  some  single  word,  tone,  or  gesture  of  the  orator.  These 
intense  master  strokes  of  action  are  characteristic  of  workmanship 
of  the  highest  order  in  all  fields  however  diverse,  as  in  trimming 
a  woman's  hat,  or  painting  a  picture;  driving  an  automobile,  or 
governing  a  nation. 

Application  of  Directive  and  Dialectic 

Similarly  in  employing  combinations  of  the  primal  instruments  of 
efficiency  it  is  of  great  importance  to  know  when  to  allow  them  to 
act  of  themselves  in  whole  or  in  part.  By  practice  their  use  in 
many  ways  may  be  made  subconscious  and  instinctive,  and  it  often 


3o6  SOURCES  OF  EFFICIENCY 

pays  not  to  interfere  with  such  methods  of  use  when  these  have 
been  acquired.  In  other  words,  often  the  most  efficient  way  of 
using  efficiental  plurahsms  is  to  treat  them  much  as  if  they  were 
living  organisms. 

Two  Principal  Forms  of  Combinations 

It  is  important  to  note  that,  in  this  relation,  highly  developed 
combinations  of  Efficients  take  two  principal  forms,  viz. :  ( i )  those 
characterized  by  peculiarly  intense  adaptations  to  the  local  pecu- 
liarities of  a  given  field,  and  (2)  more  general  and  abstract  aggre- 
gations of  the  Efficients.  It  is  well,  if  possible,  always  to  use  the 
latter  of  these  two  species  in  connection  with  the  former.  The 
close  contact  with  so-called  realities  involved  in  the  first  species, 
together  with  the  resultant  momentum  and  dynamic,  often  leads 
to  a  certain  narrowness  when  this  kind  of  combination  alqne  is 
used.  The  concurrent  application  of  the  general  ideal  species  not 
only  tends  to  prevent  these  drawbacks  but  to  produce  other  more 
positive  results  by  the  externality  thus  supplied,  and  the  interactions 
and  dialectic  which  arise  as  a  consequence. 

Universal  Efficiency  Machine 

The  general  observation  may  also  be  made  that  it  is  often  a 
source  of  efficiency  to  regard  the  entire  aggregate  of  the  Efficients  as 
a  kind  of  universal  machine,  capable  of  variation  by  marginal  reuse 
in  different  ways,  and  thus  made  applicable  to  special  problems  and 
situations. 

General  Simmiary 

At  this  point  it  will  be  of  advantage  to  sum  up  the  results  arrived 
at  in  the  present  and  preceding  chapters. 

An  efficient  process  is  one  in  which  the  results  exceed  the  expendi- 
ture.   The  primary  instrument  of  efficiency  is  the  group. 

The  group  principle  takes  several  different  forms  called  the  Effi- 
cients. Among  the  most  important  of  these  are  reuse,  the  unit  and 
multiplier,  multiplicative  groups,  orders  of  material,  uniformity  and 
diversity,  externality,  symbolism,  kinematic  and  dynamic,  directive, 
dialectic,  rhythm,  combinations,  with  limitation  and  error  as  nega- 
tive species. 

The  primary  aim  and  end  of  efficiency  is  subpersonal  surplusage 


COMBINATIONS  OF  EFFICIENTS  307 

or  positive  non-equivalence.  This  is  the  common  essence  of  value, 
happiness,  blessedness,  gain,  and  even  of  more  special  and  concrete 
terms  such  as  wealth,  fame,  food,  and  life. 

In  the  excess  of  the  result  over  the  datum,  the  idea  of  the  one 
to  the  many,  or  of  the  group,  appears  again.  Hence  many-to-oneness 
has  two  principle  aspects  (i)  that  of  the  means  or  method  (2) 
that  of  end  or  result.  In  this  double  way,  in  the  realm  of  efficiency, 
the  fundamental  principle  is  the  group. 

By  multiplicative  principle  is  meant  the  group  with  the  aspect  of 
force  or  dialectic  which  is  inherent  in  it  made  prominent,  and  hence 
suggestive  of  the  different  forms  which  the  group  assumes  and  of 
the  results  which  it  produces. 

In  order  to  apply  the  above  scheme  of  toolage,  it  is  important 
explicitly  to  recognize  that  this  scheme  is  built  on  a  full  recognition 
of  the  principle  of  limitation.  Limitation  is  primarily  subpersonal 
in  nature,  and  multiplicative  in  its  properties. 

Hence  for  efficiency  purposes  the  totality  of  things  is  to  be  re- 
garded as  composed  of  two  giant  opposed  multiplicative  systems, 
positive  and  negative,  the  one  which  produces  posiltive  rfesults 
being,  on  the  whole,  dominant. 


EXERCISE  19 

1.  Three  men  working  independently  in  one  year  earned  $3000,  $3500,  and 
$4000.  After  combining  as  a  corporation  they  together  earned  $20,000  in 
one  year.  State  the  degree  of  efficiency  involved,  and  some  of  the  Efficients 
which  might  operate  to  produce  this  result. 

2.  A  blacksmith  and  a  wheelwright  together  can  make  a  shovel  for  $2. 
This  can  be  made  in  a  factory  for  20  cents.  State  the  degree  of  efficiency 
involved  in  the  machine  made  tool  and  the  sources  of  this  efficiency. 

3.  State  the  principal  Efficients  which  make  the  aeroplane  possible. 

4.  Answer  the  same  for  the  dirigible. 

5.  What  Efficients  are  combined  in  the  modern  processes  of  spinning 
threads  and  yarn  as  compared  with  the  former  use  of  the  'distaff  and 
spinning  wheel. 

6.  What  Efficients  are  combined  in  modern  methods  of  weaving  cloth  as 
compared  with  more  primitive  mechods. 

7.  State  in  both  efficiental  and  more  conventional  terms  the  advantages  in 
using  garments  made  of  cloth  as  compared  with  the  use  of  bark  or  the 
skins  of  animals  as  clothing. 

8.  Multiply  5  bu.  2  pk.  5  qt.  by  17.  Also  multiply  427  qt.  by  17.  Estimate 
the  labor  efficiency  of  the  second  process  as  compared  with  the  first.  Name 
the  prime  sources  of  this  increased  efficiency. 


308  SOURCES  OF  EFFICIENCY 

9.  One  steamer  crossed  the  Atlantic  Ocean  in  9  days  10  hours,  and  another 
steamer  crossed  by  the  same  route  in  5  days  2  hours.  Compute  the  time 
efficiency  of  the  second  as  compared  with  the  first  steamer.  State  some  of 
the  possible  efficiental  sources  of  this  efficiency. 

10.  A  herd  of  cows  when  fed  in  a  more  or  less  haphazard  fashion  pro- 
duced $3600  worth  of  milk  in  one  year  at  a  cost  of  $2200.  Later,  when  fed 
at  the  same  expense  with  rations  compounded  scientifically,  they  produced 
$4800  worth  of  milk  in  one  year.  State  the  degree  and  sources  of  the 
efficiency  involved. 

11.  In  a  certain  poultry  establishment,  the  15,000  hens  which  are  kept  are 
divided  into  groups  of  100  each.  A  record  is  kept  of  the  daily  food  and 
number  of  eggs  laid  by  each  group.  When  the  number  of  eggs  laid  by  any 
one  group  falls  below  a  certain  standard,  the  food  of  the  group  is  changed. 
What  Efficients  are  involved  in  this  method  of  conducting  the  business? 

12.  Instead  of  paying  $600  a  year  for  a  teacher  for  his  children,  $400  for 
a  private  watchman  for  his  property,  and  $100  for  upkeep  of  roads  near 
his  property,  a  man  pays  $108  taxes.  The  financial  efficiency  of  the  second 
method  is  how  many  times  that  of  the  first?  State  the  fundamental  sources 
of  this  efficiency. 

13.  Give  an  instance  where  a  number  of  Efficients  are  in  such  close  fusion 
as  to  have  largely  lost  their  individuality. 

14.  Express  in  terms  of  the  Efficients  the  meaning  of  each  of  the  following 
conventional  categories  of  success:  foresight,  energy,  prudence,  reliability, 
popularity,  punctuality,  tact,  sagacity,  thrift,  industry,  health,  cooperation. 


CHAPTER  XVIII 

APPLICATIONS 

Many  more  or  less  concrete  applications  of  the  principles  arrived  at 
have  been  given  incidentally  in  the  preceding  pages.  It  will  throw 
new  light  on  these  principles  and  be  of  service  in  other  ways  if  a 
more  systematic,  though  brief  application  of  the  efficiency  methods 
advocated  be  made  to  specimen  departments  of  human  thought  and 
endeavor.  Since  all  applications  to  the  world  as  it  is  must,  in  the 
ultimate  analysis,  be  made  by  persons,  we  first  consider  the  relation 
of  the  principles  under  discussion  to  the  department  of  psychology. 

PSYCHOLOGY 
Memory  as  an  Efficiency  Agency 

If  a  person  can  recall  by  act  of  memory  the  way  in  which  a  given 
word  is  spelled,  he  is  often  saved  the  labor  of  going  to  the  dictionary 
and  looking  up  the  word.  In  this  and  similar  ways  one's  memory 
is  a  means  of  obtaining  economy  and  efficiency.  As  such  it  may 
have  very  great,  even  infinite  or  absolute  values.  For  example  if 
a  person  can  remember,  in  case  of  need,  the  methods  to  be  used 
in  resuscitating  a  drowned  person,  memory  may  be  the  means  of 
saving  a  life. 

It  should  also  be  added  in  this  connection  that  memory  is  groupish 
and  efficiental  in  its  organization.  For  instance  facts  are  stored 
up  by  the  mind  in  groups  and  recalled  by  means  of  this  group  rela- 
tion (called  the  association  of  ideas).  Hence  a  knowledge  of  the 
multiplicative  principle  in  its  various  ramifications  should  be  an 
aid  in  improving  the  memory  subjectively.  Objectively,  also,  a 
grasp  of  the  general  efficiental  organization  of  the  universe  will  be  an 
aid  in  recalling  and  using  any  part  of  this  whole. 

Reason  as  an  Instrument  of  Efficiency 

If  a  savage  man  observes  an  animal  floating  down  a  stream  on 
a  log,  he  may  infer  that  he  himself  can  be  transported  in  like  manner, 
and  that  thus  he  may  save  the  labor  involved  in  walking  on  the  land 
or  in  swimming.    This  one  act  of  inference,  when  fully  developed, 

309 


3IO  SOURCES  OF  EFFICIENCY 

becomes  the  whole  science  and  art  of  navigation,  and  this  simple 
instances  of  the  saving  of  labor  becomes  the  vast  and  often  transcen- 
dent fruitage  flowing  from  world  wide  travel  and  commerce.  Hence 
the  reasoning  faculty  in  man  is  an  efficiency  organ  of  great  impor- 
tance. Like  memory  it  acts  both  subjectively  and  objectively  by  the 
group  method  in  some  form.  Thus,  after  facts  have  been  arranged 
in  like  groups,  we  may  often  infer  that  what  is  true  of  one  member 
of  a  group  is  true  of  the  other  members  also.  Hence  the  reasoning 
faculty  in  man  should  be  greatly  improved  in  grasp  and  action  by 
explicit  knowledge  of  the  efficiental  group  theory  in  its  various 
aspects. 

Efficiencies  in  the  Various  Senses 

The  faculty  of  perception  in  its  elementary  form  is  so  primal 
that  it  is  difficult  of  analysis.  However  it  is  evident  that  in 
the  act  of  perceiving,  a  person  is  made  aware  of  uniformities 
and  diversities  and  hence  of  groups,  both  in  himself  and  in  the 
external  world.  To  a  certain  extent  also  in  an  act  of  perception, 
the  observer  arranges  objects  and  facts  in  groups.  Another  of  the 
services  of  perception  is  to  put  the  perceiver  directly  or  potentially 
in  useful  relations  with  externality  of  various  kinds.  In  this  respect 
the  senses  may  be  arranged  in  an  important  order  of  materials  scale. 
Thus  at  the  lower  end  of  the  scale,  the  sense  of  touch  gives  notice, 
as  a  rule,  of  somewhat  vague  and  small  externality,  w^hile,  at  the 
other  end,  the  sense  of  vision,  by  acquainting  us  with  the  fixed  stars 
for  instance,  reveals  a  highly  organized  externality  extending  for 
untold  millions  of  miles  from  the  observer. 

It  is  to  be  noted  also  that  the  organs  of  sense  act  by  the  aid 
of  various  auxiliaries  which  are  multipliers  or  group  organs  in 
essence.  Thus  the  sense  of  vision  operates  through  a  lens  embedded 
in  the  eyeball,  the  sense  of  hearing  is  aided  by  bones  which  act  as 
multiplying  levers,  and  touch  by  hairs  and  papillae  serving  in  like 
manner.  Similarly  the  efficiency  of  perception  is  often  increased  by 
external  objects  used  as  auxiliaries  and  which  concentrate  or  multi- 
ply the  data  apprehended,  illustrations  being  the  telescope,  micro- 
scope, galvanometer,  sounding  board,  and  microphone. 

Other  Psychic  Powers  as  Instruments  of  Efficiency 

In  like  manner  it  might  be  shown  that  the  imagination,  will,  and 
feelings  are  efficiental  instruments  of  different  kinds,  and  capable 


APPLICATIONS  311 

of  much  improvement  by  efficiental  methods.  In  this  connection  it 
may  be  remarked  that  what  is  often  termed  common  sense  is  per- 
ception of,  or  judgment  as  to,  primal  groups  in  the  efficiency  organi- 
zation of  things,  and  may  be  cultivated  in  the  ways  indicated  for 
the  more  conventional  psychological  powers  which  have  been 
mentioned. 

The  Group  Princ^)le  as  Fundamental  in  Psychology 

It  is  often  desirable  to  be  able  to  reduce  mental  processes,  if 
only  approximately,  to  some  single  primal  principle.  Various  mental 
categories  have  been  suggested  for  this  central  principle,  the  most 
prominent  being  feeling,  cognition,  or  volition.  But  it  is  easy  to- 
show  that  each  of  these  three  mental  categories  contains  or  im- 
plies  the  other  two.  For  example  both  action  and  feeling  in  some 
form  are  essential  elements  in  cognition.  From  our  point  of  view  the 
central  or  essential  element  of  mind  is  the  multiplicative,  or  group 
principle  operating  within  the  domain  which  we  term  personality. 
Feeling,  cognition,  volition,  and  other  mental  processes  are  certain 
specific  forms  of  this  central  principle.  According  to  efficiency  con- 
venience they  may  be  regarded  either  as  somewhat  distinct  faculties, 
or  as  the  modes  in  which  a  unitary  mentality  acts.  A  central  mental 
principle  like  that  suggested  has  important  uses  in  that  it  enables 
us  to  apply  our  knowledge  of  groups  to  all  mental  processes  and 
phenomena,  and,  for  example,  to  use  marginal  reuse  of  various 
kinds  in  dealing  with  them. 

Appreciation  of  Diverse  Psychic  Processes 

This  unitary  category  also  has  the  advantage  of  aiding  us  to  realize 
psychological  processes  widely  different  from  our  own,  as  for  in- 
stance those  of  children,  primitive  peoples,  and  the  lower  animals. 
Since  all  these  processes  are  multiplicative  and  efficiental  in  nature 
it  is  easy  to  comprehend  that  some  of  them  in  some  particular,  may 
be  far  more  highly  developed  than  our  own  corresponding  powers, 
and  also  that  animals,  for  example,  may  have  some  mental  instru- 
ments or  faculties  very  different  from  those  of  man. 

This  instrumental  view  of  mind  also  gives  us  added  insight  into 
the  processes  of  what  w^e  term  genius.  Thus  we  are  enabled  to 
realize,  for  instance,  that  every  really  great  man  is  master  in  some 
form  of  part  or  all  of  the  fundamental  efficiental  processes.    Colum- 


312  SOURCES  OF  EFFICIENCY 

bus  had  the  externality  and  directive  faculties  to  an  unusual  de- 
gree, and  Napoleon  possessed  great  powers  in  the  use  of  the  group 
principle  in  its  different  forms.  We  are  also  able  to  understand  the 
simplicity  which  characterizes  many  great  men,  since  the  mastery 
•of  even  one  item  of  the  fundamental  efficiency  processes  may  mean 
vast  power  in  the  more  concrete  world.  This  view  of  genius  also 
enables  us  to  comprehend  the  fact  that  a  great  nature  may  be  frag- 
smentary,  contradictory,  and  have  other  serious  faults,  and  yet 
produce  vastly  useful  results. 

If  mind  is  regarded  as  essentially  a  multiplicatively  grouping 
tntity,  it  is  made  easier  to  conceive  that  it,  or  the  germs  of  it,  may 
be  present  in  the  primordial  atoms,  monads,  or  substance  which 
evolution  presupposes;  or,  to  state  the  matter  in  another  form,  we 
may  conceive  of  both  mind  and  matter  as  developing  from  some 
more  primal  form  of  the  group  principle  by  radial  evolution. 

Deductions  from  Efficiental  View  of  Mind 

Specific  mention  should  be  made  of  certain  deductions  from  the 
above  views  concerning  mind,  which  are  capable  of  immediate  and 
general  application. 

( 1 )  The  view  presented  makes  obvious  the  importance  of  acquir- 
ing the  power  of  rapidly  and  accurately  reading  the  efficiental  powers 
and  habits  of  other  persons,  especially  their  externality  scope,  their 
multiplicative  grouping  faculties;  and  their  surplusage  tastes  and 
preferences.  In  other  words  the  analysis  of  the  mind  in  terms  of 
the  Efficients  should  be  made  primary  and  essential  and  that  into 
perception,  memory,  etc.,  secondary  and  auxiliary. 

(2)  The  above  view  also  shows  in  a  general  way  how  the  psycho- 
logical faculties,  as  conventionally  regarded,  may  be  greatly  improved 
in  grasp  and  efficiency.  Thus  if  the  mind  realizes  the  general  effi- 
ciency organization  of  things  as  a  whole,  a  multitude  of  new  means 
of  perceiving  uniformities  and  diversities  will  be  supplied  and  the 
faculty  of  perception  will  also  be  stimulated  to  greater  depth  and 
acuteness  of  action  by  the  realization  that  every  uniformity  or  diver- 
sity may  have  enormous  mutlipliers  with  corresponding  values  or 
dangers.  So  courage  is  greatly  increased  by  noting  that,  owing  to 
the  groupish  nature  of  the  universe,  danger  comes  only  in  spots,  and 
that,  because  of  the  dominance  of  the  positive  multiplicative  system, 
evil  tends  in  the  long  run  to  cancel  itself.    So,  also,  we  can  conceive 


APPLICATIONS  313 

•of  memory  and  reason,  feelings  and  conscience  as  developed  and 
improved  by  efficiental  means. 

(3)  The  above  view  also  makes  it  readily  conceivable  that  with 
practice,  and  often  by  the  method  of  dialectic,  new  efficiental  mental 
organs  and  powers  may  be  developed.  An  example  is  the  species 
of  pleasure  which  may  come  to  be  associated  with  an  efficiental 
process  or  fact.  Similarly  new  and  higher  processes  of  memory, 
imagination,  and  moral  judgment  may  spring  from  efficiental  data. 
We  may  conceive  also  that  powers  of  mental  grouping  and  obtaining 
results  may  be  generated  which  shall  transcend  such  terms  as  per- 
ception and  reason. 

EDUCATION 

Man's  Activities  Statable  in  Efficiental  Terms 

If  the  daily  activities  of  a  reasonably  intelligent  farmer,  for  ex- 
ample, be  examined,  it  will  be  found  that  by  far  the  greatest  part  of 
them  consists  of  acts  and  elements  such  as  have  been  described  in 
the  preceding  pages  of  this  book.  Thus  by  him  or  under  his  super- 
vision in  a  single  day  scores  or  hundreds  of  acts  of  reuse  will  be 
performed.  These  will  include  the  reuse  of  tools,  machines,  soils, 
animals,  the  farmer's  experience,  and  that  of  other  persons.  Simi- 
larly the  day's  activities  will  contain  many  uses  of  auxiliary  objects; 
of  groups  of  objects;  of  multiplicative  groups  either  in  the  form  of 
organization  as  directly  applied  to  the  work  of  the  farm,  or  of 
external  multiplicative  groups  such  as  the  post-office  system,  rail- 
roads and  various  social  and  political  organizations.  The  farmer 
will  need  to  use  symboHsms  in  keeping  his  accounts,  in  buying  and 
selling,  and  in  directing  his  subordinates.  Various  rhythms  will  be 
present  in  his  work  due  to  the  alternation  of  day  and  night,  the 
change  of  seasons,  and  the  use  of  processes  such  as  the  rotation  of 
crops.  His  work  will  also  include  many  kinds  of  directive  and  of 
utilized  motion  and  force,  and  will  be  held  in  check  by  various  forms 
of  limitation  and  error. 

Also  if  his  life  is  to  be  successful  in  the  higher  sense,  the  farmer 
must  cultivate  uniformity  in  various  forms  such  as  accuracy,  truth 
and  justice;  externality  in  the  shape  of  sympathy  and  breadth  of 
view ;  and  other  Efficients  in  various  social  and  moral  forms. 

The  successful  agriculturalist  also  needs  a  certain  amount  of 
-technical  knowledge.    Thus  a  considerable  and  more  or  less  minute 


314  SOURCES  OF  EFFICIENCY 

acquaintance  with  scientific  facts  concerning  plant  and  animal  life 
(biology)  will  evidently  be  of  service  to  him.  The  efficiency  of  his 
work  in  dealing  with  fertilizers  will  be  appreciably  increased  by  a 
knowledge  of  chemistry,  in  dealing  with  machinery  by  a  knowledge 
of  physics,  and  with  soils  by  a  knowledge  of  both  these  sciences.  Art 
acquaintance  with  psychology  or  the  principles  of  the  mind  will  be 
useful  to  him  in  commercial  operations  and  in  dealing  with  his 
employees.  But  the  larger  part,  if  not  all,  of  this  more  technical 
knowledge  is  found  on  examination  to  consist  of  the  Efficients 
clothed  or  combined  in  special  ways.  Hence  we  may  say  by  way  of 
summary  that  99  per  cent  of  a  farmer's  work  and  life  consists  of 
efficiental  processes  such  as  have  been  described  in  this  book. 

A  like  examination  would  show  that  by  far  the  larger  parts  of 
the  activities  of  other  callings,  as,  for  instance,  the  legal  profession 
or  electrical  engineering,  are,  in  like  manner,  primarily  and  essen- 
tially common  sense  efficiency  processes. 

Woman's  Activities  in  Efficiental  Terms 

It  is  equally  important  to  realize  that  the  domestic  work  of  woman 
has  a  similar  significance.  Thus  in  the  work  of  the  kitchen,  groups 
of  many  kinds  are  used  in  combining  articles  of  food  to  make  meals 
and  dishes,  in  storing  appliances  and  supplies,  and  in  systematizing 
activities.  Externalities  are  employed  in  the  form  of  utensils,  heat 
(to  produce  diversity  and  re-multiplicative-grouping),  the  experi- 
ence of  other  persons,  and  the  application  of  departments  of  knowl- 
edge like  chemistry,  physics,  biology,  agriculture,  and  ethics.  Reuse, 
either  entire  or  marginal,  occurs  in  plain  forms  such  as  the  repeated 
use  of  a  recipe  or  a  menu.  This  principle  is  also  applicable  in  less 
obvious  ways  as  when  articles  of  diet  of  different  rates  of  digestion 
are  combined  in  a  given  meal,  so  that  the  stomach  can,  in  a  measure, 
digest  them  in  succession  and  thus  reuse  its  powers.  Rhythms  are 
to  be  observed  in  the  form  of  daily,  weekly,  and  seasonal  changes 
of  work,  and  of  articles  prepared  for  food.  Directive  occurs  in 
many  different  forms  and  is  capable  of  being  made  a  source  of 
efficiency  in  many  new  ways  each  day.  Every  good  dish,  meal,  day's 
or  week's  diet  is  a  pluralism  or  combination  of  Efficients  and  in  the 
preparation  of  these  combinations  a  knowledge  of  pluralisms  may  be 
utilized  and  developed  constantly.     Similar  applications  in  kitchen 


APPLICATIONS  315 

work  of  other  Efficients  such  as  units  and  multipHers,  orders  of 
material,  and  dialectic  might  be  indicated. 

An  examination  of  other  domestic  activities  would  show  that  they 
are  statable  in  terms  like  those  just  given  for  kitchen  work  and  have 
a  like  wide  significance.  For  instance  in  house  furnishing  and  orna- 
mentation, the  externalities  and  other  Efficients  which  may  be 
employed  are  almost  without  limit.  A  similar  statement  applies  to 
dress  and  personal  adornment.  The  same  essential  artistic  and 
efficiental  principles  may  be  used  by  a  woman  in  trimming  a  hat  that 
were  applied  by  Milton  in  writing  his  Paradise  Lost.  Social  usages 
are  full  of  groupings,  regroupings,  symbolisms,  and  other  Efficients. 
This  fact  is  illustrated  by  various  social  assemblages,  by  the  recipro- 
cal reuses  at  these  of  the  efficiencies  in  which  each  person  present 
excels,  by  letters  of  introduction,  calling  cards,  bowings,  tipping  of 
hats,  shaking  of  hands,  and  by  all  that  is  included  under  such 
terms  as  tact,  courtesy,  and  friendship. 

Education  Should  be  primarily  Efficiental 

Since  life  in  general  and  work  in  different  callings  consist  essen- 
tially of  efficiental  activities,  it  follows  that  education  should  consist 
primarily  of  the  setting  free  and  development,  in  the  most  economical 
and  effective  way,  of  the  efficiental  powers  of  a  person.  This  view 
of  the  matter,  when  fully  realized,  should  lead  to  improvements  in 
the  processes  of  education,  and  should  increase  both  the  technical 
and  general  efficiental  value  of  study.  For  instance,  it  suggests  as  a 
basis  of  educational  work,  a  careful  examination  of  the  child's  mind 
with  respect  to  its  powers  and  habits  of  grouping,  multiplicative 
grouping,  reuse  and  the  other  primary  principles  of  efficiency.  It 
indicates  the  value  of  training  and  selecting  teachers  with  reference 
to  their  ability  in  developing  the  above  powers  in  children. 

Value  of  Different  Studies  in  terms  of  the  Efficients 

It  also  throws  new  light  on  the  relative  educational  value  of 
different  subjects  of  study  and  on  the  methods  to  be  followed  in 
obtaining  the  maximum  of  results  from  each  study  at  the  minimum 
of  cost.  Thus  in  linguistic  study  it  is  of  fundamental  importance  to 
realize  the  efficiental  elements  which  enter  into  the  subject.  In 
language  as  a  subject  of  study,  besides  specific  principles  of  symbol- 
ism, are  found  striking  examples  of  reuse,  groups,  multiplicative 


3i6  SOURCES  OF  EFFICIENCY 

groups,  and  all  of  the  other  Efficients.  Thus  as  an  example  of 
economy  and  reuse  we  have  the  fact  that  by  reading  a  book  of  travels 
which  costs  a  dollar  (and  often  in  fact  may  be  had  free)  we  may 
obtain  in  a  few  hours  many  of  the  results  which  could  otherwise 
be  procured  only  by  an  actual  journey  costing  hundreds  of  dollars 
and  weeks  of  time.  Marginal  reuse  is  illustrated  by  the  employment 
of  prefixes  and  suffixes  in  connection  with  word  stems.  A  book  is  a 
multiplicative  group  in  many  ways.  Since  a  large  number  of  concrete 
words  may  often  be  replaced  by  a  single  abstract  word,  the  use  of 
the  latter  illustrates  the  group  and  order  of  materials  principles. 
The  comparison  of  various  grammatical  forms  in  different  languages 
is  a  valuable  training  in  the  use  of  diversities  and  externality.  The 
fact  that  language  has  been  built  up  in  a  complex  and  bizarre 
fashion  makes  it  a  useful  representative  of  all  efficiency  pluralisms. 
It  is  well  to  note  in  this  connection  the  highly  condensed  form  and 
small  cost  of  the  subject  matter  of  linguistic  study  as  compared  with 
the  materials  employed  in  the  study  of  branches  of  science  like 
engineering  and  agriculture.  As  a  further  result  of  this  difference, 
language  study  as  a  part  of  education  has  the  advantage  that  pupils 
can  be  trained  in  it  in  large  groups  and  hence  at  small  cost. 

Most  of  the  Efficients  are  present  in  mathematical  subjects  also, 
and  often  in  a  much  more  explicit  and  detachable  form  than  in 
languages  as  ordinarily  studied.  For  a  further  development  of  this 
idea  the  reader  is  referred  to  the  various  textbooks  and  articles  by 
the  author  on  mathematical  subjects. 

As  a  subject  of  educational  study,  physical  and  biological  science 
when  compared  with  language,  has  the  advantage  of  being  in  large 
part  directly  related  with  concrete  objects  and  hence  being  free  from 
the  errors  which  arise  from  the  abstractions  and  detachment  of 
language.  In  science  also,  as  compared  with  mathematics,  the  Effi- 
cients often  appear  in  more  individual,  tangible,  and  striking  forms. 
Instances  are  externalities  in  the  form  of  various  kinds  of  appara- 
tus, the  units  and  multiplier  characteristic  of  the  experimental 
method,  and  directive  of  various  concrete  and  abstract  kinds. 

Increasing  the  Efficiency  Value  of  Studies 

The  above  analysis  not  only  indicates  methods  of  determining 
the  relative  values  of  different  studies,  but  also  suggests  methods  of 
giving  greater  usefulness  to  such  studies  as  are  selected  and  pur- 


APPLICATIONS  317 

sued.  For  instance  it  is  made  clear  that  in  the  study  of  science,  the 
Efficients  involved  in  a  process  should  be  made  as  explicit  as  possi- 
ble and  that  much  may  also  often  be  gained  by  giving  a  leading 
place  to  the  functions  and  results  of  a  process.  Frequently  it  will 
be  best  to  bring  out  the  advantageous  results  (or  efficiental  functions) 
of  a  process  first  in  a  qualitative  or  mass  form,  and  later  to  take 
up  quantitative  methods  as  a  means  of  making  results  more 
manageable  and  increasing  them  in  various  ways.  Thus  in  order 
to  interest  pupils  and  enable  them  to  get  their  efficiency  bearings,  it 
is  an  advantage  in  the  first  presentation  of  the  matter,  to  develop 
the  various  kinds  of  useful  results  which  can  be  obtained  from 
water  falling  over  a  dam.  Later  it  may  be  shown  that  the  utility  of 
these  results  will  be  greatly  increased  by  learning  the  laws  of  falling 
bodies  and  of  the  transformation  of  energy,  and  by  thus  reducing 
the  processes  involved  to  an  exact  commercial  basis. 

Informal  Efficiental  Training 

The  above  view  of  education  greatly  enlarges  the  means  by 
which  the  most  fundamental  and  important  part  of  education,  viz. 
the  development  of  the  child's  efficiental  powers,  may  be  carried  on. 
Charles  Dudley  Warner  has  said  that  a  training  in  doing  chores  has 
been  an  essential  part  of  the  development  of  every  great  man.  The 
truth  in  this  statement  is  based  on  the  fact  that  doing  chores  consists 
essentially  in  grouping  common  objects,  in  reusing  and  directing 
them,  and  in  other  primary  efficiency  processes.  Play  and  games 
may  also  be  analyzed  into  these  elements  and  hence  may  be  made 
to  have  fundamental  educational  values.  The  study  of  music,  eti- 
quette, or  even  of  changes  in  the  weather  may  be  shown  to  have 
similar  uses.  In  fact,  every  field  or  species  of  occupation,  however 
informal,  when  properly  viewed  will  prove  to  be  a  means  of  master- 
ing efficiental  methods.  This  explains  the  fact  that  many  men  have 
been  great  who  have  been  without  special  technical  training  of  any 
kind,  but  who  have  thoroughly  grasped  the  primal  efficiental  basis 
of  life.  It  also  explains  why,  after  this  basis  has  been  mastered, 
the  technique  of  one  department  after  another  may  often  be  rapidly 
assimilated  with  little  or  no  outside  help. 

Efficiency  Treatment  of  Current  Educational  Problems 

The  above  principles  of  education  are  also  an  aid  in  solving  impor- 
tant  special   problems   in   educational   methods.     Thus    effxciental 


3i8  SOURCES  OF  EFFICIENCY 

ideas  throw  light  on  the  matter  of  attention  and  interest,  on  methods 
of  discipline,  on  the  functions  of  memory,  on  the  relations  of  books 
to  things,  on  the  place  and  nature  of  heuristic  methods,  and  on  the 
best  ways  of  treating  both  defective  and  exceptionally  able  pupils. 
It  tends  to  culturize  vocational  studies  and  vocationalizes  culture 
subjects. 

General  System  of  Efficiental  Education 

Perhaps  the  view  presented  should  also  lead  to  a  radical  recon- 
struction of  the  general  system  of  education.  Thus  we  can  conceive 
of  a  study  which  underlies  and  in  a  measure  includes  the  various 
conventional  branches  and  which  essentially  consists  of  the  science, 
art,  and  philosophy  of  obtaining  results;  that  is,  of  efficiency. 

The  germs  of  this  discipline  could  be  instilled  in  the  young  mind 
during  the  processes  of  elementary  training;  its  main  outlines  would 
be  a  specific,  formal  branch  of  the  high  school  course;  in  college, 
the  thoroughly  developed  subject  could  be  taught  along  with  the 
leading  facts  and  processes  of  every  department  of  knowledge  and 
action;  in  the  university,  the  system  of  efficiency  principles  which 
had  been  thus  mastered  could  be  applied  in  learning  every  possible 
fact  about  some  one  specialty  and  in  developing  that  specialty  to  a 
new  degree  of  perfection.  It  would  seem  that  such  a  study  would 
greatly  accelerate  and  deepen  education  processes  and  enhance 
their  values. 

SOCIOLOGY 

Efficiental  Solution  of  Sociological  Problems 

From  various  points  of  view  it  is  evident  that  the  principles 
presented  in  this  book  have  important  applications  to  the  subject  of 
sociology.  Thus  the  adoption  of  the  views  under  consideration 
apparently  would  contribute  toward  the  solution  of  certain  current 
social  and  political  problems.  For  if  it  became  evident  that  all 
callings  are  analyzable  into  the  same  efficiental  elements  and  that 
consequently  the  occupations  of  cook,  engineer,  and  lawyer  are,  for 
example,  not  unlike  in  certain  essentials,  many  social  distinctions 
which  now  hinder  progress  and  limit  man's  happiness,  would  be 
largely  modified  and  perhaps  in  a  measure  would  disappear.  Among 
these  are  the  distinctions  between  higher  and  lower  social  classes, 
and  between  noble  and  menial  occupations.    Similarly  the  distinction 


APPLICATIONS  319 

between  work  and  play  would  to  a  considerable  extent  pass  away. 
For  the  two  are  resolvable  into  an  activity  which  is  back  of  and 
includes  both  of  them  as  details.  These  changes  would  make  easier 
the  distribution  of  that  residuum  of  work  necessary  in  any  social 
system;  or,  to  express  the  matter  in  another  way,  the  solution  of 
the  difficult  and  fundamental  problem  of  the  distribution  of  the 
rewards  of  human  activity  would  be  facilitated.  In  this  connection 
a  full  realization  of  the  many  costless  or  inexpensive  sources  of 
efficiental  pleasure,  power,  and  wealth  which  are  open  to  all,  is  of 
prime  importance. 

The  principles  advanced  in  this  book  also  have  an  application  to 
more  special  problems.  For  instance,  with  respect  to  race  suicide, 
it  is  made  clear  that,  apart  from  other  considerations,  in  children  are 
found  Efficients  and  efficiental  values  in  their  highest  and  best  forms. 
It  will  be  realized  that  these  far  transcend  any  values  and  pleasures 
obtainable  through  elaborate  dress,  expensive  foods,  constant  travel, 
and  other  forms  of  personal  luxury  the  fondness  for  which  is 
now  dwarfing  so  many  families. 

A  grasp  of  the  Efficients  which  constitute  the  essence  of  every 
form  of  work  would  tend  to  prevent  the  narrowing  and  blighting 
effects  of  the  division  of  labor  in  its  extreme  forms  as  now  practised. 
For  every  item  of  work  however  specific  is  seen  to  be  resolvable  into 
and  related  to  elements  of  activity  and  life  of  the  widest  possible 
significance. 

The  relation  of  the  general  conceptions  under  consideration  to  the 
problem  of  forms  of  government  has  been  considered  in  various 
places  in  the  preceding  chapters ;  other  like  applications  are  indicated 
by  such  terms  as  efficiental  wealth,  labor,  equality,  freedom,  trade 
and  competition. 

An  Efficiental  Sociology 

The  efficiency  principles  which  have  been  presented  suggest  not 
only  improvements  in  existing  social  methods,  but  also  more  funda- 
mental reorganizations.  For  these  principles,  when  fully  applied, 
mean,  on  the  one  hand,  a  new  and  more  profound  personal  free- 
dom and  development  and,  on  the  other  hand,  point  to  equally  new 
and  strikingly  effective  methods  of  cooperation  and  social  organiza- 
tion. For  if  each  person  realizes  the  fulness  of  efficiental  wealth 
available  to  him,  he  will  feel  free  and  will  be  eager  to  appreciate 
and  develop  this,  no  matter  what  views  others  may  hold,  and  this 


320      '  SOURCES  OF  EFFICIENCY 

course  when  adopted  by  individuals  will  lead  to  the  formation  of 
new  methods  of  social  cooperation.  The  efficiental  forces  tending 
to  social  reorganization  will  also  act  in  more  general  ways. 

It  is  estimated  that,  at  the  time  of  the  highest  development  of 
Greek  civilization,  every  Greek  freeman  had  on  the  average  five 
helots  or  slaves  who  worked  his  farms  and  mines  and  performed 
virtually  all  other  manual  labor  for  him.  Hence  the  Greek  freeman 
had  leisure  to  think  and  discuss  and  to  develop  the  more  abstract 
efficiental  side  of  his  life,  and  thus  to  create  an  efficiency  in  art,, 
literature,  and  philosophy  which  has  never  been  surpassed.  The 
Romans  had  equal  leisure,  but  largely  wasted  their  surplusages  in 
senseless  and  debasing  luxury.  Owing  to  the  use  of  coal  and 
machinery  some  modern  nations  have  twenty  steam  and  electric 
slaves  at  work  for  each  adult  male  citizen,  that  is  they  possess  four 
times  as  much  servile  labor  as  the  Greeks  had.  These  modern  forms 
of  surplus  energy  and  the  leisure  obtained  through  them,  are  being 
employed  in  part  as  the  Greeks  used  theirs,  in  part  as  the  Romans 
theirs,  and  partly  in  an  earnest  and  organized  search  for  still  greater 
leisure  and  power.  Hence  the  raw  material  is  already  at  hand  for  a 
far  higher  and  more  efficient  civilization  than  the  Greeks  enjoyed. 
When  the  efficiental  activities  already  in  sight  shall  have  been  fully 
coordinated  and  developed,  the  result  will  be  a  civilization  far  sur- 
passing any  the  world  has  yet  seen. 

BUSINESS 

Analysis  of  Scientific  Management  in  terms  of  the  Efficients 

In  recent  years  much  attention  has  been  given  to  the  methods  of 
conducting  business  which  have  been  termed  scientific  management 
and  which  were  largely  originated  by  Mr.  F.  W.  Taylor  of  Phila- 
delphia. Briefly  summarized  the  principles  of  scientific  manage- 
ment are  as  follows : 

1.  The  dissection  of  any  process  of  work  (as  brick  laying)  into 
its  elements  or  motions.  (In  terms  of  the  Efficients  as  presented  in 
this  book,  this  means  the  application  of  diversity  and  of  units.) 

2.  The  study  of  the  most  economical  and  efficient  way  of  perform- 
ing each  of  the  elements  in  a  given  piece  of  work.  (This  includes 
the  application  of  groupism,  multiplicative  groupism,  directive  and 
most  of  the  Efficients.) 

3.  Standardizing  the  work ;  that  is,  determining  how  much  work 


APPLICATIONS  321 

a  good  (or  bogey)  workman  following  the  most  approved  methods 
may  be  expected  to  perform  in  a  given  time.  (This  means  a  study 
of  limitations  and  specific  quality,  and  the  consequent  formation 
of  uniformities  and  multiplicative  groups.) 

4.  Instruction  of  workmen  in  the  best  methods  of  work.  (This- 
means  an  externality  and  scale  of  teachers,  and  a  reuse  of 
knowledge. ) 

5.  Selection  of  the  workmen  best  adapted  for  each  given  kind  of 
work.  (This  includes  reuse  of  work  done  by  nature,  use  of 
diversity  and  specific  quality,  and  hence  in  one  aspect  of  limitation.) 

6.  A  planning,  organizing,  and  instructing  department  of  workers 
(i.e.,  externality,  orders  of  material,  multiplicative  groups,  reuse). 

7.  Charting  and  routing  of  each  extensive  and  complicated  piece 
of  work  (i.e.,  use  of  linear  multiplicative  groups,  graphs,  and  other 
multiplicative  groups  and  symbolisms). 

8.  Sharing  the  increase  in  profits  (i.e.,  a  recognition  of  positive 
surplusage,  externality,  and  uniformity). 

By  use  of  the  above  methods,  for  example,  the  amount  of  pig 
iron  handled  by  one  man  in  one  day  has  been  increased  from  12^ 
tons  to  47  tons,  and  the  number  of  bricks  laid  from  1000  to  2700. 

Applications  of  the  Efficients  are  Wider 

From  the  above  analysis  it  is  evident  that  the  principles  presented 
in  this  book  underlie,  surround,  and  include,  so  to  speak,  the  methods 
advocated  in  the  above  system  of  scientific  management.  Hence  if 
the  individual  workman  is  familiar  with  the  Efiicients  as  such,  each 
day  numberless  ways  will  occur  to  him  in  which  he  can,  in  addition 
to  the  above  prescribed  methods,  use  the  groups,  unit  and  multiplier, 
reuse,  directive,  and  other  primal  means  to  efficiency.  The  same  is 
true  of  the  employer,  superintendents,  and  foremen. 

Furthermore  the  more  general  efiiciental  point  of  view  also  makes 
plain,  for  instance,  that  systems  of  accounting  are  but  systems  of 
multiplictive  grouping  according  to  the  categories  of  time,  place, 
material,  personality,  etc.,  and  that  a  mastery  of  the  principles  of 
multiplicative  grouping  opens  the  way  for  the  development  of  a 
special  system  of  accounting  particularly  adapted  to  any  given 
business.  The  same  statement  applies  to  all  forms  and  kinds  of 
system  and  organization  included  in  any  given  business. 

Hence  the  efiiciental  principles  stated  in  this  book  relate  not  only 
to  the  processes  of  manufacture,  but  to  those  of  buying  and  selling 


322  SOURCES  OF  EFFICIENCY 

as  well.  For  example,  the  reuse  by  other  agents  of  the  experience 
and  methods  of  the  most  successful  selling  agents  is  provided  for, 
as  well  as  the  grouping,  standardization,  and  codification  of  such 
experience  and  methods. 

Uses  af  the  Efficients  are  More  Fundamental  \ 

It  will  be  seen  that  the  principles  presented  in  this  book  will  also 
necessarily  modify  the  methods  and  processes  of  business  in  more 
fundamental  ways,  as,  for  example,  by  modifying  the  views  which 
men  hold  of  life  in  general.  Thus  a  sane  view  of  the  aims  and 
•ends  of  life  will  diminish  the  passion  for  senseless  luxury,  and  hence 
transform  the  processes  of  manufacture  and  business  which  cater 
to  such  luxury,  and  also  simplify  the  problem  of  profit  sharing. 

The  ideas  here  presented  also  aid  in  a  grasp  of  the  underlying 
principles  of  business  in  other  ways.  For  instance  every  form  of 
business  is  in  some  way  a  case  of  intake  and  output,  that  is  of 
externality  and  re-multiplicative-grouping,  with  surplusage  results. 
Hence  a  specific  knowledge  of  these  efficiental  processes  is  of  use 
throughout  the  technique  of  any  species  of  business.  Again  if  we 
view  the  universe  as  in  a  state  of  almost  exact  balance  between 
gigantic  positive  and  negative  multiplicative  systems,  the  world  is 
realized  as  a  solid  domain  of  opportunities  of  high  order  for  him 
who  is  able  to  perceive  and  utilize  such  opportunities.  Yet  the 
same  point  of  view  makes  clear  the  wisdom  of  making  it  a  rule  to  be 
content  with  large  sales  and  small  margins  of  profit,  while  at  the  same 
time  ever  being  on  the  lookout  for  a  sudden  explosive  opportunity 
due  to  some  extreme  action  of  the  multiplicative  principle.  The  law 
of  multiplication  also  makes  peculiarly  evident  the  importance  of 
holding  reserves  and  in  other  ways  being  prepared  for  sudden  ex- 
plosions in  the  commercial  world. 

Primary  Aim  of  Business 

It  is  of  equal  or  greater  importance  to  remember  that  the  aim 
of  business  is  the  making  of  positive  surplusage  in  every  possible 
way,  with  special  emphasis  on  those  ways  which  are  broad  and 
fundamental.  This  method  of  conducting  business  brings  the  largest 
and  best  returns  to  the  individual  business  man  as  well  as  to  society 
in  general.  Thus  business  is  carried  on  most  profitably  and  success- 
fully when  both  parties  to  a  bargain  are  the  gainers  thereby.  Also 
an  employer  conducts  his  business  most  successfully  when  he  con- 
siders not  only  his  technical  business  relations  with  his  employees  but 


APPLICATIONS  323 

also  their  general  welfare  and  interests,  including  their  food,  recre- 
ation, health,  education,  morals,  and  religion.  In  like  manner  em- 
ployees will  receive  the  best  pay  and  largest  rewards  of  all  sorts  when 
they  take  an  interest  in  promoting  all  the  elements  and  relations  of 
the  business  in  which  they  are  engaged. 

Similarly  an  intelligent  commercial  house  perceives  that  its  returns 
are  in  proportion  not  merely  to  the  direct  value  of  the  goods  sold, 
but  to  the  surplusage  of  all  kinds  conveyed  to  their  customers,  in- 
cluding, for  example,  the  pleasure  and  instruction  imparted  through 
works  of  art  exhibited  in  salesrooms,  through  the  artistic  presenta- 
tion of  goods,  musical  entertainment,  courtesy  of  employees,  and 
through  well  served  food  supplied  in  attractive  lunch  rooms. 

A  Universal  Practical  Instrument 

Finally  if  we  look  at  the  so-called  practical  world  as  a  whole 
the  system  of  Efficients  as  here  presented  forms  a  kind  of  universal 
tool  or  instrument,  applicable  in  some  form  to  every  problem  or 
opportunity  that  may  arise.  Thus  the  use  of  diversity,  units,  and 
groups  supplies  at  least  an  initial  method  by  which  to  attack  any 
situation.  Later,  by  marginal  variation  and  adaptation,  the  whole 
system  of  Efficients  forms  a  completer  instrumentalism  for  dealing 
with  the  developed  problem. 

ART 
General  Statement 

Since  art  is  a  special  and  somewhat  technical  form  of  symbolism, 
the  discussions  in  Chapter  X  show  in  general  how  the  principles 
under  consideration  in  this  book  have  an  application  to  various 
kinds  of  artistic  work.  If  the  matter  be  looked  into  in  more  detail, 
it  is  found  that  grasp  of  the  Efficients  helps  to  determine  the 
subject  matter  most  desirable  in  works  of  art,  the  principles  and 
forms  which  should  be  applied  to  this  subject  matter,  and  perhaps 
will  suggest  new  and  more  efficient  species  of  art.  The  result  on  the 
subjective  side  should  be  greater  ease  in  the  mastery  of  art,  added 
pleasure  and  profit  from  the  technical  appreciation  of  art,  and  still 
broader  results  owing  to  the  grasp  of  the  general  efficiental  mean- 
ings and  values  of  any  given  artistic  work. 


324  SOURCES  OF  EFFICIENCY 

Efficiental  Subject-matter 

As  to  the  subject  matter  of  art  our  point  of  view  leads  to  an 
emphatic  preference  for  constructive,  optimistic  themes.  Promi- 
nence is  to  be  given  to  that  which  is  noble  and  uplifting;  not  only 
to  that  which  is  beautiful  in  the  more  sensuous  aspect,  but  even  more 
emphatically  to  those  forms  of  beauty  which  are  capable  of  the 
most  efficiental  treatment  for  the  most  efficiental  ends.  For  instance 
the  theory  in  hand  makes  clear  that  the  dominant  part  of  Dante's 
Divine  Comedy  is  the  Paradiso,  and  that  the  greater  attention  given 
to  the  Inferno  is  due  to  a  morbid  form  of  interest,  and  to  a  lack  of 
a  grasp  of  life  in  all  of  its  relations  and  in  right  perspective. 

Efficiental  Elements  in  Highest  Forms  of  Arts 

As  to  the  forms  of  art,  the  principles  under  consideration  aid  one 
in  realizing,  for  instance,  that  mere  profusion  of  ornamentation 
cannot  produce  art  of  a  high  order.  For  such  profusion  means  only 
a  set  of  units  without  multipliers ;  or  even  worse,  an  assemblage  of 
units  which  largely  cancel  and  destroy  each  other.  In  contrast  with 
this  method  the  unit  and  multiplier  principle  would  suggest  the  use 
of  a  few  units  of  a  high  order  of  artistic  excellence  placed  on  a 
massive  and  constrained  background  which  serves  in  various  ways  as 
a  multiplier  of  the  given  units.  Such  a  combination  recognizes  the 
limitation  that  is  in  all  things,  but  it  also  has  other  more  positive 
values.  It  often  means  economy  in  material  used  and  hence  in 
cost,  and  in  energy  expended  by  the  observer  in  learning  to  under- 
stand and  appreciate  a  given  work.  More  important  still,  large 
margins  or  backgrounds  constitute  an  externality  of  space  in  which 
self  activity  can  function,  and  at  the  same  time  challenges  and  stimu- 
lates this  self  activity  to  fill  in  details,  and  to  propagate  and  develop 
the  given  units  according  to  personal  taste  or  need.  Similar  results 
are  obtained  by  an  atmosphere  of  twilight  or  by  any  "noble  dim- 
ness", in  connection  with  one  or  more  well  developed  units  of  art 
symbolism. 

In  like  manner  other  Efficients  are  often  found  to  be  fundamental 
sources  of  power  in  works  of  art  of  a  high  order.  An  important 
case  of  the  use  of  groupism  in  art  is  the  combination  of  several  suc- 
cessive phases  or  elements  of  an  act  or  process  in  a  single  picture 
or  statue.  This  principle  is  strikingly  illustrated  in  many  of  the 
works  of  the  sculptor  Rodin.  So  in  literature  the  mere  use  of 
"words,  words,  words"  is  additive,  while  the  use  of  "local  habitation 


APPLICATIONS 


325 


and  a  name"  is  multiplicative.  This  principle  is  widely  illustrated 
by  the  almost  paradoxial  importance,  in  any  linguistic  statement, 
of  the  small  words,  like  since,  thus,  hence,  for  etc.,  which  are  em- 
ployed to  denote  space,  time,  number,  cause,  and  other  prime  group 
relations,  and  whose  right  use  is  essential  to  a  clear  presentation 
of  the  multiplicative  group  essence  of  a  subject. 

An  examination  of  works  of  art  of  the  highest  order  also  seems 
to  suggest  that  each  of  these  contains  some  expression  or  indica- 
tion of  infinite  externality.  This  characteristic  is  illustrated,  for 
instance,  by  the  Sistine  Madonna  as  contrasted  with  the  Madonna  of 
the  Chair.  In  the  first  of  these  paintings,  the  mother  of  Christ  is 
gazing  at  something  distant  and  inspiring,  perhaps  at  the  epoch- 
making  work  to  be  performed  by  her  son,  or  at  the  source  of  this. 
Another  illustration  of  this  principle  of  a  widely  different  type 
is  the  avenue  of  trees  receding  in  the  distance  in  Hobbema's  Avenue 
of  Middleharnais. 

Efficiental  Elements  in  Other  Departments  of  Art 

This  suggestion  of  infinite  vistas  of  expansion  and  development 
is  also  found  in  various  forms  in  literature  of  high  order.  In  fiction 
one  of  the  most  subtle  and  powerful  of  these  forms  is  that  super- 
poise  of  the  author  by  which  he  is  enabled  to  project  his  characters 
against  the  background  of  the  general  efficiental  organization  of 
things,  to  measure  them  thus  in  various  ways,  and  to  suggest  their 
further  development.  In  accordance  with  this  principle  also  we  find 
the  highest  type  of  literature,  not  in  Shakspere,  in  spite  of  his  mar- 
velous profusion  of  local  excellence,  nor  in  Dante's  Inferno,  so 
vivid  in  its  artistic  qualities  but  so  negative  in  its  main  content,  but 
in  Dante's  Paradiso  with  its  spiral  unlimited  development  of  the 
individual  soul. 

Similarly  other  of  the  Efficients  are  often  present  in  great  works 
of  art  in  more  striking  form.  When  thus  present,  they  not  only 
govern  the  form,  but  also  constitute  the  most  important  part  of  the 
subject  matter.     Hence  in  them  form  and  content  coalesce. 

It  is  well  to  note  in  this  connection  that  each  of  the  fine  arts 
contains  certain  characteristic  efficiental  elements.  Thus  orchestral 
music  of  a  high  order  is  a  swiftly  changing  combination  of  systems  of 
groups  and  other  Efficients  which  is  highly  educative  as  well  as  the 
source  of  the  noblest  pleasure. 


326  SOURCES  OF  EFFICIENCY 

Schools  of  Art 

It  is  evident  that  in  such  conceptions  different  schools  of  art  find 
a  common  principle  or  essence;  that  in  the  beauty  of  a  primal  and 
perhaps  ultimate  efficiency,  realism  and  idealism,  truth  and  beauty 
as  ordinarily  understood,  utility  and  art  merge  or  melt  together. 
Thus  the  highest  art  expresses  a  pure  surplusage  which  is  indepen- 
dent of  time  and  of  any  eccentricity  of  personal  or  national  mood. 
This  form  of  art  is  approximated  by  an  object  like  the  Parthenon 
which  gives  the  impression  of  being  neither  large  or  small,  young 
or  old.  This  pure  efficiental  art  may  be  regarded  as  at  times  acting 
in  special  channels  and  thus,  on  occasion,  giving  rise  to  certain 
individual  forms  or  schools  of  art,  each  having  its  own  peculiar 
efficiencies,  examples  being  the  classical,  romantic,  and  impression- 
ist schools. 

Advantages  of  Efficiental  View  of  Art 

This  view  of  the  matter  leads  to  varied  and  often  profound  mar- 
ginal reuse  in  the  appreciation  of  art.  It  also  greatly  enlarges  the 
scope  of  artistic  expression  and  pleasure.  Thus  the  furnishings  of  a 
home,  while  in  themselves  simple  and  inexpensive,  may  be  made 
to  express  artistic  data  of  the  first  importance,  as,  for  instance,  the 
various  efficiental  principles.  The  same  statement  applies  to  the 
architecture  and  the  external  surroundings  of  the  home,  to  dress 
and  personal  adornment,  and  to  speech  and  personal  manners.  So 
also  Ruskin  has  shown  that  the  sky  and  clouds  form  a  changing 
picture  gallery  to  the  properly  trained  eye,  and  he  and  others  have 
made  clear  that  the  same  is  true  of  the  landscape  both  as  a  whole 
and  in  its  details.  The  ideal  aimed  at  in  the  whole  field  of  rela- 
tively unconventional  art  is  that  the  individual,  the  home,  the  town 
or  city,  and  nature  shall  each  radiate  positive  surplusage  in  a  con- 
tinuous esthetic  form. 

The  principles  arrived  at  in  the  preceding  discussion  also  enable 
us  to  conceive  of  the  possibility  of  new  and  higher  forms  of  art  than 
those  in  current  use.  Such  forms  may  express  efficiental  themes 
to  efficiental  sensuous  powers  in  efficiental  ways  for  efficiental  ends, 
more  explicitly  and  effectively  than  do  the  current  types  of  art. 


APPLICATIONS 


327 


ETHICS 

Efficiency  in  Christian  Ethical  Principles 

If  we  examine  Christ's  injunction  to  return  good  for  evil  we  find 
that,  apart  from  other  considerations,  the  principle  involved,  in  the 
long  run,  is  a  highly  efficient  one,  and  far  more  so  than  the  princi- 
ple of  retaliation.  For  the  fruits  of  retaliation  are  single  or  local 
and  negative,  while  the  mode  of  life  implied  by  the  forgiveness  of 
injuries  is  positive  and  means  a  continuous  radiation  of  positive 
surplusage  in  spite  of  all  injustice  or  misunderstandings,  and  hence 
is  superior  to  retaliation  in  a  dual  infinite  way  in  its  general  effi- 
ciency properties.  An  examination  of  the  other  paradoxical  ethical 
principles  taught  by  Christ  would  show  that  they  have  similar  effi- 
ciency properties.  i 

Efficiency  in  Various  Fundamental  Principles  in  Ethics 

In  like  manner  if  we  consider  the  various  ideas  which  have  been 
proposed,  from  time  to  time,  as  a  fundamental  principle  of  a  system 
of  ethics,  we  shall  find  that  each  of  the  more  meritorious  of  these 
possesses  efficiency  properties  of  a  high  order.  This  is  true  of  such 
primal  ethical  concepts  as  knowledge,  harmony,  moderation,  benevo-* 
lence,  sympathy,  utility,  altruism,  complete  life,  and  happiness. 
Almost  or  perhaps  all  of  these  it  will  be  noted,  directly  or  indi- 
rectly, mean  fundamental  groupism  of  some  sort. 

Efficiental  Analysis  of  the  Different  Virtues 

In  like  manner  it  may  be  shown  that  the  different  virtues,  so- 
called,  have  efficiental  values  of  the  first  importance.  Thus  for 
instance  modesty  is  a  realization  of  diversity,  externality,  and  limita- 
tion, and  has  the  uses  connected  with  these  principles.  Truthfulness 
has  the  values  which  come  from  a  correspondence  (or  uniformity) 
between  fact  and  symbol ;  patience  those  of  externality  and  dialectic ; 
sympathy  and  generosity  those  of  externality  and  groupism.  In  fact 
the  virtues  may  be  arranged  in  groups  according  to  the  Efficients 
prominent  in  them.    Thus  we  have 

(i)  The  externality  group,  containing  altruism,  love,  self-denial, 
modesty,  reverence,  patience ; 

(2)  The  directive  group,  containing  charity,  generosity; 

(3)  The  order  of  materials  group,  of  good  will  or  motive,  charac- 
ter, intention; 


328  SOURCES  OF  EFFICIENCY 

(4)  The  uniformity  group,  of  honesty,  truthfuhiess,  justice; 

(5)  The  diversity  and  limitation  group,  of  chastity,  temperance. 
The  more  conventional  classification  of  virtues  in  groups  relating 

(I)  to  the  individual,  (II)  to  other  persons  and  (III)  to  God,  may 
be  regarded  as  essentially  a  grouping  with  respect  to  different 
degrees  of  externality. 

Solution  of  Ethical  Problems 

The  above  analysis  of  ethical  principles  in  terms  of  the  Efficients, 
aids  in  the  solution  of  certain  ethical  problems.  One  of  these  is 
the  problem  of  the  relation  of  self-interest  to  altruism.  In  cases 
where  these  two  principles  seem  to  be  in  conflict  the  proper  course 
to  follow  would  seem  to  be  that  which  would  produce  the  greatest 
and  highest  surplusage  independently  of  personal  considerations. 
Sometimes  self-development,  and  in  other  cases  a  primary  atten- 
tion to  the  interests  of  others  will  do  this.  In  order  to  decide  be- 
tween these  courses  in  specific  cases,  much  study  of  the  peculiarities 
of  the  given  situation  is  necessary,  such  study  being  conducted  as 
far  as  possible  in  terms  of  the  fundamental  categories  of  efficiency. 
At  times  a  point  is  reached  where  self-interest  and  altruism  merge, 
or  are  lost,  in  the  deeper  principle  of  the  subpersonal  or  non- 
jective  making  of  positive  non-equivalence  in  all  possible  ways  at 
all  times. 

Advantages  in  the  Efficiental  View  of  Ethics 

So  also  from  the  efficiental  standpoint,  certain  new  developments 
of  the  conventional  virtues  are  possible,  and  also  perhaps  the  for- 
mation of  what  may  be  termed  new  virtues,  with  new  vices  corre- 
sponding to  them.  Thus  any  perfected  mastery  of  an  Efficient  might 
be  an  efficiental  virtue;  and  any  habitual  or  intentional  violation  of 
the  same,  an  efficiental  vice.  We  are  also  enabled  to  arrive  in  this 
way  at  the  conception  of  a  summun  bonum  or  goal  of  all  effort  such 
as  has  been  indicated  in  other  places. 

A  farther  advantage  of  the  above  efficiental  treatment  of  virtues, 
vices,  and  ethical  principles  seems  to  be  that  it  can  be  embodied 
in  systems  of  education  without  running  counter  to  personal  or  re- 
ligious bias  in  such  matters.  It  also  aids  in  the  mastery  and  appli- 
cation of  these  principles  in  other  ways.  Rightly  understood  it  adds 
a  new  imperativeness  to  moral  laws. 


APPLICATIONS  329 

RELIGION 
Efficiency  Values  of  Religion 

Whatever  his  views  as  to  conventional  religions  and  doctrines, 
every  one  must  admit  that  abundant  evidence  exists  of  the  effi- 
cacious results  which  frequently  follow  the  use  of  that  vast  and 
unbounded  externality  implicit  in  every  religion  worthy  of  the  name. 
The  word  religion  means  a  relaying  or  regrouping,  and  this  re- 
grouping in  connection  with  and  under  the  influence  of  infinite 
externality  often  leads  to  extraordinary  efficiency  results.  These 
have  many  times  been  illustrated  in  the  phenomena  of  religious 
conversions. 

The  efficiency  values  in  religion  have  however  often  been  greatly 
obscured  by  the  abuses  which  from  time  to  time  have  grown  up  in 
connection  with  religious  principles.  These  abuses  have  frequently, 
indeeed,  been  of  a  gravity  which  corresponded  to  the  enormous 
power  for  good  inherent  in  an  efficiental  use  of  infinite  externality, 
and  constitute  a  striking  illustration  of  the  law  of  rhythm  and 
backeddyism. 

An  examination  of  the  conventional  doctrines  and  ceremonies 
which  characterize  various  religions  would  show  that  each  of  these 
technical  details  and  outward  forms  is  usually  the  source  of  cer- 
tain special  efficiencies  though  often  marred  in  practice  by  drawbacks 
and  evils.  But  the  detailed  examination  of  these  matters  lies  be- 
yond the  scope  of  this  book. 

Advantages  of  the  Efficiental  View 

The  above  method  of  viewing  religion  possesses  certain  advantages, 
which  should,  at  least,  receive  mention.  For  instance  it  opens  the 
way  to  a  free  and  aggressive  development  of  the  primary  and  fun- 
damental values  in  religion  apart  from  those  questions  as  to  details 
and  outward  forms  which,  in  the  past,  have  been  the  source  of  so 
much  bitter  conflict.  Perhaps  it  makes  possible  the  study  of  such 
values  as  a  part  of  a  general  system  of  education. 

Possibly  also  it  should  lead  to  the  development  of  some  religious 
ideas  into  higher  and  transcendent  forms.  Thus  as  an  outcome 
of  it  we  can  conceive  of  new  ways  of  clothing  infinite  externality 
with  auxiliary  efficiental  toolages.  These  in  turn  may  react  on  the 
principles  which  they  aid,  the  result  being  fruitages  or  categories 
of  value  of  which  we  cannot  now  form  an  adequate  conception. 


330 


SOURCES  OF  EFFICIENCY 


General  Outlook 

The  above  statement  concerning  the  efficiency  meaning  of  reli- 
gion, concludes  our  illustrative  application  of  the  principles  arrived 
at  in  the  preceding  chapters,  to  certain  specimen  departments  of 
human  knowledge  and  action.  These  prime  agents  of  efficiency 
might,  of  course,  in  like  manner  be  applied  to  other  departments 
of  life  and  thought.  The  principle  of  limitation  will,  apparently,  be 
always  at  work,  but  if  the  universe  be  regarded  as  a  combination  of 
two  multiplicative  systems,  one  positive  and  the  other  negative,  in 
proportion  as  the  negative  one  is  overcome,  the  positive  system  will 
predominate  in  accelerating  multiplicative  fashion,  with  correspond- 
ing fruitages  which  cannot  be  fully  anticipated. 


EXERCISE  20 

General  Review 

1.  On  a  given  machine  an  efficiency  engineer  found  that  compared  with  what 
it  should  have  been,  the  width  of  the  cutting  point  of  the  tool  was  %,  the 
speed  was  Y^,  and  the  amplitude  of  the  stroke  4  times  (i.e.  the  stroke  over- 
ran threefold).     Express  the  efficiency  of  the  machine  as  a  per  cent. 

2.  A  crop  of  600  bushels  of  corn  which  might  have  been  sold  at  84  cents 
a  bushel  was  fed  to  farm  animals  and  was  thus  made  worth  $1120.  If  the 
labor  of  feeding  coist  $84,  compare  the  efficiency  of  the  two  methods  of  dispos- 
ing of  the  corn.    What  Efficients  are  involved  in  the  second  process? 

3.  When  potatoes  were  raised  without  spraying,  on  a  given  field,  it  cost 
$4000  to  raise  a  crop  worth  $6400.  A  crop  produced  in  a  later  year  was 
sprayed  at  an  additional  cost  of  $400  and  was  worth  $8800.  State  as  a  per 
cent  the  efficiency  of  the  first  crop  in  terms  of  the  second. 

4.  What  Efficients  are  involved  in  the  process  of  reducing  fractions  to  a 
common  denominator  and  adding  them? 

5.  If  a  modern  cotton  gin  and  compress  are  operated  by  one  half  the 
number  of  men  required  by  a  former  type  and  turn  out  twice  as  much  baled 
cotton,  express  the  labor  efficiency  involved. 

6.  A  city  factory  was  using  1500  tons  of  soft  coal  per  year  thirty  per  cent  of 
which  went  up  the  chimney  as  smoke.  Later,  after  installing  a  smoke  consum- 
ing grate  and  by  utilizing  some  of  the  gases  which  had  gone  up  the  chimney, 
the  amount  of  coal  was  reduced  to  1050  tons.  State  the  degree  of  fuel  effi- 
ciency involved.  State  also  the  Efficients  employed  and  indicate  the  resulting 
dialectic. 

7.  What  principles  of  efficiency  are  used  by  a  housekeeper  who  buys  eggs 
when  they  are  cheap  and  keeps  them  in  liquid  glass  till  they  are  dear? 

8.  What  principle  of  efficiency  was  involved  when  a  primitive  man  in 
making  a  fire  accidently  melted  copper  and  tin  ore  together  and  thus  made 
bronze? 


APPLICATIONS  331 

9.  State  in  efficiental  terms  the  different  methods  of  making  "a  little  go  a 
long  way". 

Explain  the  efficiental  meaning  of  each  of  the  following: 

10.  There  are  more  ways  of  killing  a  dog  than  hanging  him. 

11.  Patience  and  shuffle  the  cards   (Spanish  proverb). 

12.  The  early  bird  gets  the  worm. 

13.  Give  ham  rope  enough  and  he  will  hang  himself. 

14.  He  can't  see  farther  than  the  end  of  his  nose. 

15.  Fine  feathers  don't  make  fine  birds. 

16.  By  indirection  find  direction  out. 

17.  All  waste  comes  from  isolation  of  some  sort. 

18.  Sweet  are  the  uses  of  adversity. 

19.  He  has  something  up  his  sleeve. 

20.  Explain  the  advantage  to  a  business  man  of  keeping  his  capital  as  far 
as  possible  in  a  fluid  state. 

21.  To  a  general  of  keeping  his  forces  concentrated  as  far  as  possible. 

22.  Why  is  a  street  corner  near  the  center  of  a  city  usually  a  superior 
location  for  a  place  of  business. 

23.  What  is  the  reaison  for  the  statement  that  it  does  not  make  so  much^ 
difference  what  subject  we  study  as  how  we  study  it. 

24.  In  terms  of  the  Efficients  discuss  the  utilities  in  play.  How  could  a 
knowledge  of  the  Efficients  be  made  a  means  of  increasing  these  utilities? 

25.  State  the  advantages  in  having  one  man  in  a  factory  distribute  the 
supplies  to  the  machines  before  the  work  is  begun,  as  compared  with  having 
the  workmen  who  use  the  supplies  go  to  the  store  room  for  them  as  they  are 
needed. 

26.  Explain  the  efficiency  significance  of  the  motto  "e  pluribus  unum".  Also 
of  "non  multa,  sed  multum". 

Explain   in   efficiental   terms. 

27.  The  advantage  to  a  large  firm  in  employing  a  general  purchasing  agent. 

28.  The  meaning  of  the  phrase,  cross  fertilization  of  the  sciences. 

29.  The  advantages  and  disadvantages  of  combining  several  small  businesses 
as  a  corporation, 

(i)  With  reference  to  the  owners  of  the  business; 

(2)  To  the  employees ; 

(3)  To  the  general  public. 

30.  What  Efficients  make  it  possible  to  photograph  a  star  which  cannot  be 
seen  through  the  best  telescope. 

31.  Explain  the  source  or  sources  of  efficienc}"^  in  watching  the  eye  of  a 
boxer  instead  of  his  hands. 

State  the  various  Efficients  prominent  in  the  subject  of 

32.  Arithmetic  33.  Algebra  34.  Geometry 

35.  Physics  36.  Botany  37,  Language  study 

38.  Before  the  appearance  of  the  Colorado  beetle  a  farmer  in  raising 
potatoes  spent  $26  per  acre  and  produced  87  bushels  per  acre.     After  the 


332  SOURCES  OF  EFFICIENCY 

appearance  of  the  beetle,  he  spent  $42  and  raised  170  bushels  per  acre.  Com- 
pare the  efficiency  of  the  two  processes.  State  the  sources  of  increased  effi- 
ciency. 

39.  Napoleon  estimated  his  own  presence  with  one  of  his  armies  as 
equivalent  to  the  addition  of  100,000  common  soldiers  to  its  strength.  Explain 
as  far  as  you  can  the  efficiency  of  Napoleon  as  compared  with  a  common 
soldier. 

40.  Explain  the  sources  of  efficiency  in  the  use  of  a  bicycle  as  compared 
with  walking. 

41.  Explain  as  far  as  you  can  the  non-equivalence  between  the  energy  used 
in  pulling  the  trigger  of  a  gun  and  the  energy  in  the  action  of  the  bullet. 

42.  It  is  estimated  that  the  cost  of  human  unskilled  labor  is  1000  times  the 
cost  of  the  same  work  when  done  by  the  best  steam  engine.  Name  the  princi- 
pal reasons  for  his  difference. 

43.  State  in  efficiental  terms  the  meaning  of  each  of  the  following  elements 
of  success :  honesty,  intelligence,  accuracy,  self-reliance,  loyalty,  shrewdness, 
courage. 

44.  State  in  efficiental  terms  the  advantages  of  knowing  the  cause  or  causes 
of  an  event.  Also  in  knowing  the  results  of  a  process  'before  they  happen. 

45.  Give  the  efficiental  reasons  for  the  following  statement:  At  a  certain 
stage  in  a  process  of  thought  a  certain  vagueness  of  thought  is  useful. 

46.  Diiscuss  in  terms  of  the  Efficients  the  reservoirs  of  power  unconsciously 
possessed  by  every  person. 

47.  Discuss  the  meaning  of  the  following  statement :  "Culture  is  that  which 
is  left  after  you  have  forgotten  everything  which  you  have  learned." 

48.  Explain  the  advantage  in  not  trying  to  remember  everything  but  only 
where  everything  may  be  found. 

49.  Also  in  not  trying  to  form  once  for  all  a  system  which  shall  include 
every  detail  and  situation  of  life  but  rather  in  having  the  means  of  making 
a  system  in  any  given  situation. 


APPENDIX 

A.     THE  CATEGORIES  AND  A  GENERAL  PHILOSOPHY 

OF  LIFE 
Preliminary  Illustration 

Beside  the  prime  sources  of  efficiency  which  have  been  investi- 
gated in  the  preceding  pages,  certain  other  abstract  and  general 
instruments  of  thought  and  action  have  long  been  in  use  which  it 
will  be  of  advantage  to  examine,  if  only  briefly.  As  an  illustration 
we  may  take  the  category  of  space. 

If  a  set  of  pigeonholes  is  used  for  any  given  purpose  it  is  usually 
much  more  convenient  to  arrange  the  set  of  compartments  in  the 
form  of  a  square  or  rectangle  rather  than  in  linear  order.  Among 
the  advantages  which  result  from  the  areal  arrangement  are  the 
economy  to  eye  and  hand  in  using  the  system  owing  to  the  fact  that 
the  distance  between  any  two  pigeonholes  is  greatly  diminished  on 
the  average.  Also  after  long  use  of  such  an  arrangement,  other 
benefits  arise  such  as  the  utilization  of  various  positional  symbolic 
relations  and  various  other  groupages. 

Similarly  other  areas,  as  the  wall  of  a  room  or  the  surface  of 
a  farm,  in  time  are  often  instinctively  realized  as  saturated  with 
facile  reciprocal  externalities  and  highly  condensed  groupages  of 
many  kinds,  from  which  various  dialectics  result  which  would  not 
be  possible  with  a  merely  linear  object.  Hence  a  surface  is  fre- 
quently, if  not  always,  a  special  efficiency  instrument  of  great  power. 

The  above  illustration  may  be  extended  to  space  of  three  dimen- 
sions. For  if  a  set  of  drawers  be  constructed  each  of  which  consists 
of  a  rectangularly  arranged  set  of  pigeonholes  (or  checkerboard 
arrangement  of  some  sort),  we  shall  have  a  still  higher  conden- 
sation (or  groupism)  of  parts,  with  a  consequent  higher  manifold 
and  more  facile  externaHty  and  a  dialectic  of  cross  multiplicative 
groupings.  In  this  way  we  are  brought  to  realize  that  space  itself, 
from  a  certain  point  of  view,  is  an  efficiency  instrument  of  great 
importance;  that  it,  in  effect  is  a  multiplicative  group  system  of 
three  orders,  manifold,  continuous,  and  saturated  with  many  result- 
ing efficiency  properties.     This  conception  of  space  is  an  important 

333 


334  SOURCES  OF  EFFICIENCY 

aid  in  mastering  the  properties  of  space  as  commonly  understood, 
in  conceiving  of  additional  properties  possessed  by  it,  and  in  making 
the  most  effective  use  of  all  these  properties  as  sources  of  efficiency. 

General  Statement 

A  like  point  of  view  holds  with  respect  to  other  and  perhaps  all 
of  the  so-called  categories,  such  as  time,  cause,  reality,  substance,  and 
quality.  These  entities  may  often  be  usefully  regarded  as  special 
instruments  of  efficiency.  They  may  have  been  evolved  in  a  some- 
what haphazard  way,  but  with  respect  to  certain  uses  they  have 
been  developed  to  a  high  pitch  of  instrumental  power,  accompanied, 
however,  by  equally  high  degrees  of  danger  and  limitation,  A  study 
of  the  more  important  of  these  categories  from  this  point  of  view 
will  not  only  be  of  direct  advantage  but  will  be  useful  as  an  aid  in 
removing  certain  fundamental  and  pervasive  efficiency  errors,  such  as 
the  tendency  on  the  one  hand  to  overuse  the  category  of  personality, 
^nd  on  the  other  those  of  mechanism  and  equivalence  reality.  Hence 
such  a  study  should  be  an  aid  to  the  appreciation  and  extended  use 
of  the  broadest  and  most  permanent  kind  of  efficiency,  as  distin- 
guished from  that  which  is  narrow  and  personal.  It  will  also  be  an 
aid  in  relating  the  idea  of  efficiency  to  other  approximately  ultimate 
ideas,  and  realizing  its  place  in  a  general  scheme  or  philosophy 
of  life. 

The  categories  under  consideration  are  so  interwoven  in  meaning 
that  it  is  necessary  to  discuss  each  of  them  more  or  less  in  terms  of 
the  others,  it  being  noted  that  our  main  object  is  to  obtain  efficiency 
results,  and  that  the  development  of  a  simple  filiar  system  among 
the  concepts  studied  is  merely  secondary  and  auxiliary  to  the  main 
purpose.  However  the  cancellations  and  other  dialectic  results  which 
arise,  will  produce  this  filiar  ordering  of  the  categories  to  a  certain 
extent. 

Classification  of  the  Categories 

It  will  be  an  advantage  first  to  make  an  approximate  grouping  of 
the  categories  to  be  examined.  This  classification  will  be  made 
primarily  with  reference  to  certain  leading  Efficients.  We  thus 
obtain 

I.  The  Reality,  or  Uniformity  Group,  consisting  of  the  concepts. 
Reality,  Substance,  Matter. 


CATEGORIES 


335 


11.  The  Quantity,  or  Pure  Group,  containing  Quantity,  Space, 
Number,  Infinity,  Zero. 

in.  The  Quality,  or  Diversity  Group,  containing  QuaHty,  Time, 
Order,  Negation. 

IV.  The  Dynamic,  or  Motion  and  Force  Group,  consisting  of 
Motion  and  Force,  Change,  Cause,  Teleology. 

(The  category  of  Teleology  also  forms  a  transition  link  to  the 
next  group.) 

V.  The  Vital  or  Directive  Group,  containing  Life,  Mind,  Personal- 
ity, Subject  (vs.  object). 

VI.  The  Absolute  Group,  in  which  the  principle  of  orders  of 
material  is  carried  to  an  extreme  development.  It  contains  such 
concepts  as  the  Absolute,  Fundamental,  and  Ultimate. 

I.      REALITY   GROUP  OF   CATEGORIES 
Matter 

It  has  been  said  by  a  certain  scientific  worker  that  the  carbon 
molecule  and  other  chemical  elemental  ideas  are  mere  concepts 
(i.e.,  primal  groups)  to  enable  us  to  deal  more  efficiently  with  phe- 
nomena, and  that  the  whole  idea  of  matter  itself  is  merely  a  sec- 
ondary and  auxiliary  phenomenon.  It  is  important  to  realize  more 
definitely  from  the  efficiency  standpoint,  what  is  meant  by  these 
and  like  statements. 

As  an  illustration  of  the  utility  inherent  in  the  idea  of  materiality 
and  substantiality  and  similar  concepts,  we  may  take  Democritus' 
theory  of  vision  and  the  various  useful  results  which  have  followed 
from  it.  According  to  this  theory  any  given  object  is  constantly 
giving  off  effluvia  in  the  shape  of  fine  atoms ;  and  when  these  atoms 
enter  the  eye  they  produce  an  impression  (or  image)  which  results  in 
the  given  object  being  seen.  With  all  its  imperfections  this  theory 
has  the  merit  of  suggesting  that  something  exists  between  the  eye 
and  the  object  seen,  and  that,  by  directing  or  working  with  this 
something,  the  process  of  vision  may  in  a  measure  be  controlled  and 
made  more  efficient.  For  instance,  it  is  but  a  step  from  this  view  to 
the  thought  that  by  interposing  a  lens  between  the  eye  and  the 
seen  object  the  atomic  effluvia  from  objects  may  be  collected  and 
vision  so  powerfully  reinforced  that  the  very  distant  or  the  very 
minute  be  made  visible  as  in  the  telescope  and  microscope;  or  to 
Newton's  idea  that  the  corpuscles  given  off,  if  they  be  of  different 


336  SOURCES  OF  EFFICIENCY 

sizes,  may  be  sorted  into  groups,  the  prismatic  colors  and  spectrum 
analysis  being  the  result. 

If  we  enlarge  this  idea  of  atoms  given  off  by  objects  to  the  con- 
ception of  a  universal  fluid  in  which  all  objects  are  immersed  and 
which  objects  can  cause  to  undulate  in  various  ways,  we  have,  in 
general,  the  modern  idea  of  the  ether.  Regarding  the  ether  as 
having  certain  of  the  properties  of  materiality,  Faraday  formed  the 
idea  that  a  forward  thrust  of  the  ether  in  one  direction  would  result 
in  a  backward  thrust  in  some  nearby  adapted  channel,  or  what  is 
called  the  principle  of  electrical  induction.  The  efficiency  outcome 
of  this  was  the  invention  of  the  dynamo,  and  of  electrical  machinery 
in  general.  It  also  resulted  in  Clerk  Maxwell's  electro-magnetic 
theory  of  light,  and  wireless  telegraphy. 

Hence  we  may  take  John  Stuart  Mill's  conception  of  matter, 
viz. :  as  the  permanent  possibility  of  sensation,  and  extend  it  into 
the  statement  that  matter  is  the  permanent  possibility  of  groupisms. 
and  efficiencies  of  certain  specific  sorts.  From  this  point  of  view 
matter  means  the  combined  use  of  externality  in  both  space  and 
time,  of  multiplicative  groups  (see  for  instance  the  various  methods 
of  dividing  and  subdividing  and  combining  parts  of  matter),  of 
rhythms  and  other  positive  Efficients,  along  with  limitations  or 
special  qualities  such  as  are  implied  in  the  terms  impenetrability, 
incompressibility,  and  inertia.  The  various  scientific  theories  of 
matter,  such  as  the  ethereal  stress  and  strain  theory,  and  the  molecu- 
lar-atomic hypothesis,  in  like  manner  may  be  viewed  as  special 
combinations  or  aspects  of  the  toolage  properties  of  matter. 

It  is  ever  to  be  borne  in  mind  that  while  the  concept  matter  is 
thus  a  powerful  efficiency  agent  in  certain  relations,  it  also  has 
connected  with  it  serious  dangers  and  limitations.  Thus  the  over 
use  of  it,  or  the  crude  use  of  it,  may  prevent  the  recognition  and 
application  of  other  important  sources  of  efficiency  in  a  given  case. 

Flowever  the  dangers  will  be  somewhat  prevented  if  instead  of  the 
conventional  somewhat  crude  and  lumpish  view  of  matter,  we  sub- 
stitute the  above  view  which  makes  matter  a  special  combination, 
of  the  Efficients  and  hence  a  special  instrument  of  efficiency. 

The  view  of  the  categories  of  matter  and  substance  here  advo- 
cated also  opens  the  way  to  using,  aggressively  yet  safely,  these 
categories  as  special  sources  of  efficiency  under  some  circumstances. 
Thus  when  forms  of  abstract  groupism  have  become  familiar,  it 


CATEGORIES 


337 


is  frequently  a  source  of  added  efficiency  to  regard  them  as  possessing 
certain  of  the  attributes  of  materiality,  or  as  more  or  less  substan- 
tial, and  thus  to  obtain  the  advantages  of  being  able  to  manipulate 
such  forms  swiftly,  readily,  and  by  a  low  order  of  force,  and  also  of 
conceiving  them  as  always  at  hand  and  ready  to  act  of  themselves 
in  certain  ways. 

By  emphasizing  or  otherwise  modifying  one  or  more  of  the 
efficiental  elements  which  go  to  make  up  the  concept  of  matter,  it 
is  possible  readily  to  conceive  of  different  species  of  matter,  and  also 
of  different  degrees  of  materiality,  and  then  to  use  these  widely 
in  the  special  efficiency  channels  for  which  they  are  adapted. 

Substance  and  Reality 

By  substance  is  ordinarily  meant  a  substratum  underlying  the 
special  qualities  of  an  object;  or  that  which  is  left  after  an  object 
has  been  stripped  of  its  so-called  qualities  and  attributes.  Hence 
the  idea  of  matter  may  be  refined  and  generalized  into  that  of  sub- 
stance; or  substance  may  take  the  special  form  of  matter.  Thus 
substance  is  a  kind  of  prime  group,  or  efficiency  abstract  essence  of 
matter  and  other  objects.  Hence  much  that  has  been  said  about  the 
efficiental  nature  and  uses  of  matter  applies  also  with  slight  modifi- 
cations to  the  category  of  substance. 

The  concept  of  reality  differs  from  that  of  substance  in  that  reality 
often  has  connected  with  it  the  idea  of  positive  and  aggressive  action, 
while  substance  is  mainly  negative  or  resistant.  In  the  reality 
concept  the  mechanical  triggerlike  properties  which  are  prominent 
in  the  categories  of  matter  and  substance  are  less  explicitly  developed. 
The  term  reality,  since  it  is  applicable  to  ideal  entities,  as  to  thoughts 
and  forces,  is  far  broader  in  scope  than  are  matter  and  substance  in 
their  conventional  connections.  Looked  at  more  independently, 
reality  from  our  point  of  view,  is  the  possibility  of  permanent  and 
certain  reuse.  Thus  when  we  say  that  a  specified  man  or  entity  is 
the  real  thing,  we  mean  that  he  or  it  can  be  depended  upon  as  a 
source  of  vital  and  fundamental  efficiencies. 

It  follows  that  the  efficiencies  involved  in  the  categories,  matter, 
substance,  and  reality  form  an  approximate  order  of  materials  suc- 
cession, increasing  in  abstractness  and  comprehensiveness. 

So  valuable  are  the  efficiencies  contained  in  the  idea  of  reality  and 
so  widely  are  these  applicable,  that  in  many  cases  this  concept  has 
come  to  be  regarded  as  the  most  fundamental  source  of  efficiency, 


338  SOURCES  OF  EFFICIENCY 

and  has  even  at  times  been  so  overused  as  to  exclude  all  other 
methods  of  obtaining  results  except  as  subordinate  details.  In  this 
connection  may  be  noted  the  tendency  to  regard  the  discovery  of  one 
fundamental  reality  as  the  aim  of  all  philosophic  study,  even  of 
life  itself. 

As  an  aid  in  preventing  an  exaggerated  emphasis  of  the  reality 
concept,  it  is  well  to  keep  in  mind  the  defects  of  this  concept  as  an 
agent  of  efficiency.  It  is  to  be  remembered  that  the  reality  concept 
is  characterized  by  a  tendency  to  premature,  crude,  and  exclusive 
finality,  by  a  lack  of  diversity,  and  by  a  certain  negative  or  resistant 
element.  These  limitations  tend  constantly,  so  to  speak,  to  fossilize 
the  concept  in  hand. 

Viewing  the  category  of  reality  as  a  special  aggregate  of  efficien- 
cies opens  the  way  to  the  idea  of  different  degrees  and  forms  of 
reality,  and  hence  to  a  wider  use  of  the  concept  in  its  efficiency 
relations. 

II.      QUANTITY    GROUP    OF    CATEGORIES 

Space 

In  the  preceding  series  of  categories  the  concept  of  matter  was 
taken  and  refined  and  generalized,  primarily  with  reference  to  our 
sense  of  touch.  In  like  manner  we  may  refine  and  extend  it 
primarily  with  respect  to  our  sense  of  vision,  and  we  shall  thus  arrive 
at  the  concepts  of  space  and  quantity.  Space  then  is  a  special  effi- 
ciency method  of  treating  objects  or  entities  of  any  kind,  as  was 
indicated  in  the  opening  paragraphs  of  this  chapter. 

Other  considerations  may  be  adduced  which  will  be  an  aid  in 
realizing  as  subordinate  and  auxiliary  that  view  which  regards  space 
as  an  object  or  thing  (that  is,  the  substance  or  thinghood  aspect  of 
space).  A  misapprehension  of  the  purpose  with  which  the  first 
treatises  on  the  properties  of  space  were  written,  is  largely  respon- 
sible for  the  exaggerated  emphasis  on  the  latter  aspect  of  the  above 
category,  and  for  the  desire  for  absolute  certitude  which  springs 
from  this  view.  The  title  of  the  first  systematic  treatise  on  space, 
viz. :  the  one  written  by  Euclid,  is  Elements  of  Geometry,  and  the 
word  here  translated  Elements  is  exactly  the  same  word  which 
the  early  Greek  philosophers  used  when  they  described  the  universe 
as  composed  of  the  elements  earth,  air,  fire  and  water.  In  other 
words,  just  as  the  Greek  philosophers  sought  to  reduce  the  physical 
universe  to  systematic   form  and  thus  by  the  use   of   uniformity 


CATEGORIES 


339 


and  diversity  and  by  various  kinds  of  groupisms,  to  economize 
man's  labor  in  mastering  and  extend  his  power  of  manipulating 
it,  so  Euclid's  primary  purpose  v^as  to  reduce  the  various  properties 
of  space  to  a  few  primal  units,  and  thus  give  man  an  efficient  mastery 
of  the  multitudinous  variety  of  geometrical  facts.  Flawless  certi- 
tude of  deduction  was  secondary  and  auxiliary  in  accomplishing 
this  primary  end.  Similarly  his  so-called  axioms  were  named  by 
him  "common  notions";  that  is,  by  them  he  meant  general  and 
primal  groups,  or  agents,  in  obtaining  results,  not  primal  elements  of 
certitude.  If  two  things  are  equal  to  the  same  thing,  we  are  able 
to  save  the  labor  of  a  direct  comparison  of  the  two  things.  Simi- 
larly two  points  form  a  simple  and  highly  efficient  representative 
of  a  straight  line;  and  three  points,  of  a  plane.  In  like  manner  it 
might  be  shown  that  all  the  different  definitions  and  theorems  of 
geometry  are  each  an  individual  agent  of  efficiency,  and  that  the 
combination  of  these  into  a  system  is  made  merely  with  a  view 
to  obtaining  a  higher  order  of  efficiency.  It  will  be  found  also  that 
space  may  be  regarded  as  a  multiplicative  system  built  up  out  of 
different  elements  in  an  unlimited  variety  of  ways. 

One  advantage  of  the  above  view  is  that  it  facilitates  the  forma- 
tion and  recognition  of  a  great  number  of  different  kinds  of  space, 
and  also  the  groupings  of  any  given  set  of  objects  so  as  to  form 
what  is  in  effect  a  space,  and  thus  of  reusing  our  knowledge  and 
grasp  of  ordinary  space  in  order  to  obtain  increased  efficiency  in 
treating  an  aggregate  of  given  objects.  For  example,  if  sensations 
be  classified  according  to  their  differences  in  quality,  intensity,  and 
duration,  they  may  be  grouped  and  treated  as  a  space.  Similarly  we 
are  able  to  conceive  of  degrees,  germs,  and  seeds  of  spatiality,  and  to 
make  these  ideas  sources  of  efficiency  under  certain  circumstances. 

Number 

In  like  manner  from  the  efficiency  point  of  view,  numbering  is 
more  important  than  number,  number  itself  being  but  a  special 
existential  tool  aspect  or  element  in  numbering.  In  other  words,  the 
category  of  number  is  to  be  regarded  primarily  as  a  method  or 
instrument  for  obtaining  efficiency,  rather  than  as  a  static  object. 
Hence  it  is  important  to  realize  so  far  as  possible  the  efficiental 
components  of  the  category  of  number. 

Evidently  the  unit  and  multiplier  principle  constitutes  a  special 
case  or  application  of  number.     Also  in  its  more  general  aspect 


340  SOURCES  OF  EFFICIENCY 

number  is  to  be  regarded  as  a  form  of  linear  multiplicative  groups 
characterized  by  the  uniformity  among  its  elements,  by  their  sepa- 
rateness  or  discreteness,  and  by  the  special  and  highly  efficient  form 
of  symbolism  used  in  representing  them.  This  symbolism  obtains  its 
efficiency  from  the  uniformity  in  the  size  of  the  unit  symbols  em- 
ployed, from  the  extreme  use  of  the  principle  of  neighborhood 
symbolism,  and  from  the  fact  that  the  symbolism  for  each  number 
indicates  not  only  a  magnitude  but  also  a  position  in  a  scale.  Be- 
cause of  its  relative  simplicity  and  wide  applicability  the  number 
toolage  becomes  highly  assimilated  in  the  mind  and  often  acts  with 
great  inherent  speed  and  force,  and  with  dialectic  power.  An 
illustration  is  the  way  in  which  the  reuse  method  termed  generaliza- 
tion frequently  acts  of  itself,  when  the  number  concept  or  a  few 
number  symbols  are  present  with  given  material. 

The  efficiencies  connected  with  number  are  so  important  that 
the  presence  of  number  in  some  form  seems  necessary  to  a  high 
degree  of  efficiency  in  the  treatment  of  any  domain  of  material. 
Thus  Plato  says,  "If  arithmetic,  mensuration,  and  weighing  be  taken 
away  from  any  art,  that  which  remains  will  not  be  much."  In  like 
manner  Lord  Kelvin  says,  "I  often  remark  that  when  you  can 
measure  what  you  are  speaking  about  and  express  it  in  numbers, 
you  know  something  about  it;  but  when  you  cannot  measure  it  in 
numbers,  your  knowledge  is  of  a  meagre  and  unsatisfactory  kind; 
it  may  be  the  beginning  of  knowledge,  but  you  have  scarcely  in  your 
thoughts  advanced  to  the  stage  of  science."  In  another  connection 
by  way  of  illustration,  Kelvin  adds,  "Arrhenius  did  not  originate 
the  doctrine  of  electrolytic  dissociation  or  of  free  ions;  that  was 
enunciated  in  1857  by  Clausius,  and  remained  relatively  barren. 
What  Arrhenius  did  was  to  introduce  measured  quantities  into  the 
doctrine,  and  show  its  simple  quantitative  applicability  to  aqueous 
solutions;   immediately  it  became  fertile." 

Quantity 

The  category  of  quantity  differs  in  general  from  space  and  number 
in  that  it  is  of  a  higher  and  more  abstract  order  and  for  many  effi- 
ciency purposes  may  be  regarded  as  including  the  two  categories 
just  treated  as  special  cases.  Hence  much  that  has  been  said  of  space 
and  number  is  true  also  of  quantity,  but  with  the  difference  that  the 
efficiental  elements  and  properties  of  quantity  are  more  general 
and  comprehensive.     In  particular  it  should  be  noted  that  quantity 


CATEGORIES 


341 


is  characterized  by  an  unlimited  possibility  of  uniformities,  diver- 
sities, groups,  and  multiplicative  groups.  Its  pervasiveness  also  adds 
to  its  importance  as  an  instrument  of  efficiency. 

Zero  and  Infinity 

The  conventional  meaning  assigned  to  zero  is  that  of  absence  of 
quantity  or  substantiality  of  any  particular  kind.  But  to  obtain  the 
full  efficiency  significance  of  the  term,  the  context  (or  externality) 
associated  with  a  zero  in  any  particular  case  must  be  considered. 
For  instance  an  absence  of  the  kind  described  is  often  due  to  a 
concentration  of  material  in  a  process  of  group  making.  Hence 
such  absences  and  emptinesses  are  often  closely  associated  with 
corresponding  groupages,  and  these  absences  may  become  important 
instruments  of  efficiency  in  connection  with  the  corresponding  group- 
ages.  Thus  a  person  may  often  express  his  intentions  or  attitude 
in  a  highly  efficient  way  by  doing  nothing.  A  Fabian  policy  is  an 
approximation  to  this  method  of  obtaining  results.  A  more  abstract 
case  is  the  use  of  x  for  ix'^. 

Much  more  important  is  the  fact  that  zero  frequently  means  a 
balance  between  two  opposites,  these  opposites  often  being  two 
extensive  and  highly  developed  multiplicative  systems.  The  zero 
involved  may  be  made  a  source  of  efficiency  in  connection  with  these 
systems  in  various  ways.  For  instance  when  we  can  write  0  =  0  —  a, 
if  we  know  or  can  control  one  of  the  a's,  we  can  often  learn  or 
control  the  other  with  little  or  no  expenditure  of  effort.  In  other 
words,  often,  where  only  blankness  apparently  is  present,  two  equal 
and  opposed  systems  may  really  be  at  work,  and  the  wise  use  of 
these  two  systems  in  relation  to  each  other  may  be  made  the  source 
of  efficiency.  Also,  frequently  a  convenient  and  powerful  way 
of  applying  externality  is  to  substitute  for  zero  or  emptiness  two 
equal  and  opposed  aggregates  of  some  kind. 

For  efficiency  purposes,  infinity  is  best  regarded  as  the  group 
principle  acting  without  limit,  either  as  to  the  extent  of  its  action  or 
in  some  other  respect.  Hence  it  is  primarily  a  method  rather  than 
an  object.  Nevertheless,  as  with  other  categories,  the  thinghood 
aspect  of  infinity  has  certain  special  uses  under  special  circumstances. 
Thus  the  idea  of  infinite  externality  as  an  object  has  a  more  re- 
straining and  stimulating  effect  for  certain  persons  in  some  forms 
of  religion  than  infinity  as  a  principle  or  method.  The  objectivity 
form  of  the  infinity  concept  however  brings  with  it  peculiar  dangers 


342  SOURCES  OF  EFFICIENCY 

also,  such  as  its  tendency  to  crush  and  overwhelm,  or  at  least  to 
create  a  feeling  of  mere  dependence.  On  the  other  hand  infinity 
when  viewed  as  unlimited  groupism  is  easier  to  grasp,  and  can  be 
applied  more  widely  and  freely.  This  view  also  opens  the  way  to 
devise  infinities  of  various  sorts  and  to  reuse  the  specific  efficiency 
grasp  which  we  already  have  of  this  category. 

III.     THE    QUALITY    AND    TIME    GROUP    OF    CATEGORIES 

Quality 

A  quality  of  an  object,  for  our  purpose,  is  to  be  regarded  pri- 
marily as  an  extremely  close  resultant  of  a  number  of  efficiental 
elements.  Thus  hardness  (as  of  a  piece  of  glass  for  instance) 
means  force,  acting  particularly  as  a  Hmitation  to  other  specific 
forces,  and  hence  persistence  in  time,  and  hence  certain  group-making 
powers  (as  with  respect  to  the  transmission  of  light  and  heat).  It 
is  to  be  noted  that  the  frequent  difficulty  of  analysing  a  quality  into 
various  elements  is  often  an  advantage  in  that  it  enables  us  quickly 
and  readily  to  manipulate  qualities  by  the  use  of  a  low  order  of  force. 
It  may  however  be  a  disadvantage  because  of  the  lack  of  diversity 
which  it  entails. 

A  broader  and  often  more  useful  view  is  that  which  regards 
qualities  and  objects,  when  considered  together,  as  forming  a  reci- 
procal group  system.  According  to  this  view  an  object  is  com- 
posed of  a  substratum  (or  underlying  substance)  in  which  a  number 
of  qualities  inhere.  Also  any  one  quality  may  be  present  in  many 
different  objects,  and  therefore  bind  these  objects  together  as  a 
group.  Thus  glass  has  the  qualities  of  hardness,  transparency,  a 
certain  specific  gravity,  etc.  But  transparency  is  a  property  of 
other  objects  besides  glass,  as  of  water,  air,  alcohol,  quartz  crystals, 
etc.  A  danger  in  this  view  of  the  matter  is  that  it  brings  the  idea 
of  substance  into  what  is  perhaps  an  unduly  prominent  position. 
At  the  same  time  other  dual  reciprocal  group  relations  involved 
tend  to  diminish  this  danger. 

A  realization  of  quality  as  essentially  groupistic  in  nature  should 
increase  its  value  as  an  instrument  in  obtaining  efficiency.  For 
example,  in  a  soil  the  quality  of  fertility  is  composed  of  a  group  of 
component  qualities  such  as  the  physical  qualities  of  looseness,  and 
cohesion,  and  other  textural  properties;  also  of  certain  chemical 
properties  due  to  the  presence,  in  right  proportions,  of  nitrogen, 


CATEGORIES  343 

phosphorus,  potash,  and  other  elements;  also  of  certain  biological 
qualities  due  to  the  presence  of  the  proper  bacteria.  A  knowledge 
of  these  elements  of  fertility  gives  great  efficiency  in  rendering  a 
given  soil  more  productive. 

Time 

For  efficiency  purposes  time  is  to  be  regarded  as  a  special  method 
of  grouping  phenomena.  This  multiplicative  grouping  is  usually 
regarded  as  predominantly  linear  in  form,  though  there  is  a  sense 
in  which  time  may  be  regarded  as  of  two  or  more  dimensions,  or 
even  as  a  stratum  or  other  detail  in  some  more  comprehensive 
multiplicative  group  system.  Hence,  as  with  space  and  number, 
the  substantiality  aspect  of  time  is  merely  special,  incidental,  and 
etv^en  superficial.  Since  time  is  often  used  as  a  symbol  for  one  or 
more  forces,  it  forms  a  convenient  transition  to  the  next  group  of 
categories  to  be  considered. 

IV.      THE  DYNAMIC   GROUP  OF   CATEGORIES 
Force  and  Motion 

The  categories  of  force  and  motion  were  discussed  at  length  in 
chapter  XII  (p.  210)  and  are  now  referred  to  again  merely  with  a 
view  to  safeguarding  their  use  from  certain  errors  and  to  developing 
their  more  efficient  use  with  reference  to  certain  of  the  categories 
under  discussion  in  this  chapter.  For  instance,  a  motion  takes 
place  in  space  and  time,  and  the  remarks  which  have  been  made 
concerning  space  and  time  in  the  present  chapter  should  render  the 
utilization  of  motion  more  accurate  and  fruitful. 

Mechanism  and  Cause 

In  the  idea  of  mechanism  the  groupages  which  are  characteristic 
of  matter  and  force  are  combined  to  produce  certain  new  groupages 
and  efficiencies,  often  higher  and  more  intense  than  the  component 
ones.  Thus  when  a  domain  of  material  has  been  reduced  to  the 
mechanical  state,  large  parts  of  this  domain  can  be  operated  in  a 
trigger-like  way  at  a  slight  cost  of  effort  and  by  a  low  order  of 
force.  Hence,  in  certain  relations,  mechanism  is  a  highly  useful 
source  of  efficiency.  It  is  probably  universally  applicable  in  some 
forms  or  aspects.  Hence  it  has  often  been  the  tendency  to  overuse  it, 
just  as  its  components,  matter  and  force,  have  been  overused;  at 
times  to  make  it  the  primary,  fundamental,  and  perhaps  exclusive 


344  SOURCES  OF  EFFICIENCY 

method  of  obtaining  results;  or  even  to  regard  it  as  something 
final  in  itself  and,  by  overuse  to  the  point  of  contradiction,  exclu- 
sive of  the  very  idea  of  surplusage  in  results.  As  a  matter  of  fact 
from  what  has  already  been  said  in  connection  with  matter  and 
force  it  follows  that  mechanism  holds  a  subordinate  and  super- 
ficial place  in  the  general  scheme  of  groupage. 

A  few  additional  words  may  also  be  said  in  regard  to  the  category 
of  cause.  As  has  already  been  remarked,  for  our  purpose  the  cause 
of  an  event  is  best  regarded  as  a  precedent,  dynamic  externality  to 
the  event.  Hence  a  grasp  of  the  causes  of  a  fact  is  an  important 
means  of  obtaining  efficiency  results.  For  instance,  such  a  grasp  is 
often  an  important  aid  in  systematizing  knowledge,  or  in  directing 
processes.  In  many  cases  a  cause  may  be  regarded  as  a  handle  by 
which  to  control  or  even  create  effects.  But  here  again  it  is  to  be 
remembered  that  there  is  nothing  final  or  ultimate  in  the  idea  of 
causation,  and  that  it  is  merely  an  item  or  aspect  in  the  general 
scheme  of  groupage. 

Teleology 

The  category  of  teleology  forms  a  convenient  transition  to  the 
next  group  of  categories  to  be  considered.  The  aims  and  ends  of 
efficiency  processes  have  already  been  discussed  at  length  in  Chapter 
IX  (p.  152)  and  this  matter  of  teleology  (or  final  cause)  is  now  re- 
ferred to  again  only  with  a  view  of  so  restating  the  matter  in  con- 
nection with  certain  other  categories  as  to  make  it  safe  to  use  this 
principle  more  aggressively  for  efficiency  purposes  than  is  often 
done  in  some  connections.  From  the  point  of  view  here  prominent, 
an  aim  (or  final  cause)  is  an  externality  which  subjectively  precedes 
but  which  objectively  follows  an  act.  In  the  past  undue  prominence 
has  often  been  given  to  immediate,  personal  aims  and  results.  Per- 
sonality is  frequently  very  capricious  and  erratic  in  its  operations. 
Hence  teleology  which  consists  of  personal  aims,  uses,  and  values  has 
often  led  men  into  the  grossest  errors.  As  a  consequence  numerous 
scientific  workers  and  investigators  have  gone  to  the  other  extreme 
and  sought  to  discard  all  teleology,  and  thus  have  lost  the  help, 
often  powerful,  which  is  inherent  in  this  particular  species  of 
externality  when  properly  applied.  The  kind  of  teleology  which  is 
always  safe  to  apply  and  which  is  almost  invariably  productive  of 
useful  results,  is  subpersonal,  efficiental  teleology.  This  consists  of 
aiming  to  obtain  groups  and  other  Efficients,  and  hence,  ultimately. 


CATEGORIES  345 

surplus  of  some  kind.  Almost  all  important  results  in  scientific  inves- 
tigations in  the  past  have  been  obtained  by  the  use,  consciously  or 
unconsciously,  of  some  teleologic  aim  of  this  kind.  In  this  class 
of  purposes  belongs  the  aim  of  discovering  uniformities  and  diversi- 
ties, and  later  of  classifying  facts  in  groups.  A  higher  species  is 
the  aim  to  obtain  a  good  working  hypothesis  and  later  to  develop 
it  into  a  final  theory  (or  multiplicative  group  system).  More  specific 
illustrations  are  the  studies  which  Harvey  made  of  the  uses  of  the 
valves  in  the  blood  vessels  and  which  helped  him  to  his  discovery  of 
the  circulation  of  the  blood,  and  Darwin's  investigations  of  the  pur- 
poses and  uses  of  parts  of  organisms  in  connection  with  the  survival 
of  the  fittest  and  the  evolution  of  forms  of  life.  From  the  point 
of  view  here  advocated,  it  should  be  an  aid  in  obtaining  results  in 
all  fields  of  work  to  regard  the  discovery  and  development  of  groups, 
multiplicative  groups,  externality,  and  other  Efficients,  as  a  certain 
primal,  subpersonal  aim  and  end  of  processes.  As  has  already  been 
suggested,  we  can  in  this  connection  even  conceive  of  one  final  and 
comprehensive  aim  or  summum  bonum,  viz. :  a  thoroughly  perfected 
and  universal  groupage  yielding  the  utmost  surplusage  to  every 
entity  and  mode  of  existence.  If  not  itself  final,  this  aim  should 
form  an  aid,  not  a  hindrance,  in  obtaining  a  more  ultimate  result. 

V.      THE  DIRECTIVE  GROUP  OF  CATEGORIES 

We  now  come  to  a  group  of  categories  closely  related  to  the  Effi- 
cient termed  directive.  This  group  includes  the  categories  con- 
ventionally known  as  life,  mentality,  personality,  and  subject  (vs. 
object). 

Life 

For  our  purpose  a  living  organism  may  be  regarded  as  essen- 
tially a  set  or  domain  of  groups  combined  and  acting  in  certain 
specific  ways.  In  it  directive,  externality,  and  rhythm,  and  resulting 
surplusages  are  prominent.  As  has  already  been  indicated  in  various 
places  such  aggregates  have  connected  with  them  certain  character- 
istic limitations  and  aptitudes  for  error  commensurate  with  the 
extraordinary  powers  inherent  in  them. 

If  life  be  thus  viewed  as  consisting  of  certain  essential  and  specific 
groupages  it  becomes  easy  to  conceive  of  a  great  variety  of  forms 
of  life  many  of  them  widely  different  from  those  usually  included 
under  this  term.     Thus  looking  at  the  matter  from  the  chemical 


346  SOURCES  OF  EFFICIENCY 

standpoint,  just  as  our  present  terrestrial  life  seems  based  on  carbon 
groupages,  so  it  seems  possible  to  conceive  of  a  system  of  life 
based  on  silicon  groupages,  and  hence  to  conceive  of  life  of  this 
kind  as  present  in  the  hottest  stars.  Similarly  we  may  conceive  of 
vital  groupages  different  in  many  non-chemical  ways  from  those 
familiar  to  us  on  the  earth,  as  present,  for  instance,  on  the  planet 
Mars  or  other  planets.  Similarly,  by  development  of  the  groupages 
involved,  we  may  conceive  of  far  higher  orders  and  degrees  of 
life  than  any  with  which  we  are  at  present  acquainted. 

If  the  category  of  life  be  viewed  essentially  in  the  above  way,  it 
also  becomes  easy  to  reuse  our  present  grasp  of  this  source  of  effi- 
ciency in  an  aggresive  and  somewhat  artificial  way.  Thus  we  gain 
a  certain  confidence  in  the  use  of  some  Efficients  and  groupage 
aggregates  by  regarding  them  as  agents  possessing  powers  of  inde- 
pendent action,  and  to  be  relied  upon  to  produce  results  of  them- 
selves. We  may  even  regard  them  as  endowed,  in  a  sense,  with 
some  attributes  of  personality  or  even  of  hyper-personality. 

Mind 

In  continuance  of  the  above  views  mind  may  be  regarded  as 
life  plus  (or  with  an  especial  development  of )  a  high  order  of  ex- 
ternality and  directive.  Consciousness,  as  is  indicated  by  the  ety- 
mology of  the  word  {con,  meaning  together,  and  scio,  to  know) 
is  a  knowing  of  things  together,  or  an  awareness  of  them  in  groups ; 
and  mind  is  a  development  and  use  of  these  groups  with  reference 
to  a  varied  and  increasing  externality.  Hence  it  is  easy  to  see  that 
mind  must  be  an  efficiency  instrument  of  the  highest  order  of 
importance.  This  view  of  mind  enables  us  to  conceive  of  a  great 
variety  of  mentality,  including  types  very  different  from  those 
familiar  to  us  in  human  beings;  as,  for  instance,  of  methods  of 
sense  perceptions  in  the  animals  widely  different  from  those  in 
man,  and  also  of  very  superior  and  transcendent  mental  processes 
perhaps  attainable  in  time  by  us  and  perhaps  glimpsed  in  the  intel- 
lectual processes  of  so-called  geniuses.  It  also  enables  us  to  make 
certain  aggressive  and,  in  a  sense,  artificial  uses  of  mentality  similar 
to  those  suggested  for  the  category  of  life. 

Personality  is  life  and  mind  in  connection  with  a  single  organism 
and  usually  developed  in  some  striking  and  specific  way. 

By  subject,  in  this  connection,  is  meant  a  personality,  as  con- 
trasted with  the  rest  of  the  universe,  or  some  part  of  it,  taken  as 
object. 


CATEGORIES  347 

VI.       THE   CATEGORY   OF   THE   ULTIMATE   OR   ABSOLUTE 

Efficiency  Properties  of  an  Absolute 

If  we  could  discover  a  primal  (ultimate,  fundamental,  central, 
dominating)  category  or  entity,  in  terms  of  which  all  other  entities 
could  be  stated,  or  from  which  they  could  be  derived,  we  should  evi- 
dently have  a  highly  important  source  of  efficiency.  For  if  this 
fundamental  entity  should  prove  to  be  a  thing  or  object,  by  con- 
trolling or  directing  it  we  could  reduce  the  universe  to  a  mechanical 
or  triggerish  state.  If  it  were  more  abstract  in  nature  it  would  still 
furnish  an  all-comprehensive  unity  (or  uniformity),  with  vital  and 
comprehensive  uses  such  as  that  of  furnishing  the  material  or 
basis  for  unlimited  group  formations,  or  that  of  supplying  an  omni- 
present and  manifold  externality,  or  that  of  opening  the  way  to 
universal  marginal  reuse.  Because  of  this  inviting  vista  a  large  part 
of  the  history  of  human  thought  has  consisted  of  the  search  after 
some  one  fundamental  reality  with  the  (often  subconscious)  hope  of 
obtaining  a  single  final  and  complete  instrument  of  efficiency  or 
means  of  obtaining  results.  Various  names  have  been  suggested  for 
this  primal  category  among  these  being  the  fundamental  reality, 
truth,  or  principle ;  the  ultimate  reality,  or  the  absolute. 

It  may  be  suggested  at  this  point  that  the  present  investigation 
thus  far  points  to  the  conclusion  that  all  that  is  useful  in  the  pro- 
posed category  of  efficiency  now  under  discussion  is  obtained  by 
taking  the  group  concept  itself  as  the  ultimate  and  inclusive  principle 
for  the  present. 

In  this  connection  it  may  be  noted  that  if  we  examine  the  various 
ultimate  principles  which  have  been  suggested  in  the  past,  we  find 
that  each  of  these  may  be  regarded  as  a  modification  or  aspect  of 
the  group  principle. 

List  of  Proposed  Absolutes 

These  suggested  ultimates  may  be  classified  as  follows: 

I.  The  materialistic  class :  matter,  water,  air,  fire. 

II.  The  force  or  energy  class:  energy,  force,  light  (and  dark- 
ness), motion,  change. 

III.  The  biologic  class:    life. 

IV.  The  psychological  or  personal  class  :  mind,  reason,  conscious- 
ness, pleasure,  love,  faith,  will,  idea,  spirit,  soul,  God. 

V.  The  ethical  and  practical  class :    good,  duty,  value. 


348  SOURCES  OF  EFFICIENCY 

VI.  The  methodological  class :  becoming,  evolution,  the  way, 
unity,  number,  the  category  of  order,  relation,  interaction,  or 
system. 

VII.  The  reality  class:     absolute,  substance,  being. 

The  Multiplicative  Principle  as  a  Provisional  Absolute 

The  analysis  virhich  has  already  been  made  in  this  chapter  of  the 
various  categories,  and  also  that  made  of  other  of  the  above  con- 
cepts in  the  course  of  preceding  chapters,  shows  in  a  general  way  in 
what  sense  each  of  the  above  proposed  ultimate  principles  may  be 
regarded  as  a  special  form  or  modification  of  the  group  principle. 
When  the  multiplicative  principle  is  taken  as  ultimate,  the  narrowness 
or  special  individuality  of  many  of  these  primal  categories  is  reme- 
died by  the  tendency  to  expansion  which  is  characteristic  of  the 
group  idea.  For  instance,  the  multiplicative  principle  by  its  power 
of  self-correction  and  of  developing  unity,  remedies  the  chaotic  ten- 
dency inherent  in  a  personality  or  an  ethical  principle  when  each 
one  applies  it  to  suit  himself,  as  when  each  one  forms  his  own  sys- 
tem of  values. 

For  this  and  other  reasons,  by  regarding  each  of  the  above  pro- 
posed central  principles  as  a  modification  of  the  group  principle,  the 
way  is  opened  to  use  each  of  them,  and  the  system  derived  from  it, 
aggressively  as  a  special  form  of  instrumentation. 

It  is  also  to  be  noted  that  if  something  more  underlying  and  in- 
clusive than  the  multiplicative  principle  is  discoverable,  the  expan- 
sive and  corrective  properties  of  this  principle  would  seem  to  lead 
on  to  and  to  compel  the  attainment  of  this  something  in  the  end, 
in  case  such  attainment  is  possible.  Hence  we  arrive  at  the  con- 
clusion that  for  the  present  the  largest  results  are  to  be  obtained 
by  regarding  the  group  or  multiplicative  principle  as  the  most 
ultimate  in  sight,  and  by  viewing  personality  (in  the  conventional 
sense  of  the  term),  reality,  thinghood,  and  all  forms  of  equivalence 
as  relatively  secondary  toolages. 

The  Categories  in  General 

With  respect  to  the  categories  as  a  whole,  it  should  be  remarked 
that  each  of  them  probably  contains  something  characteristic  and 
unique,  which  may  at  any  time  become  the  source  of  hitherto  un- 
realized efficiencies;  and  also  that,  by  modification  of  the  diflferent 
categories  and  by  various  combinations  of  them,  what  are  in  effect 


CATEGORIES  349 

important  new  and  more  or  less  independent  species  of  them  may 
be  obtained. 

Phenomena 

Before  closing  the  discussion  of  the  categories,  some  mention 
should  be  made  of  what  are  conventionally  known  as  phenomena; 
that  is,  of  sights,  sounds,  and  other  sensations  and  perceptions,  and 
of  the  objects  which  are  taken  as  directly  represented  by  these.  Since 
phenomena  may  be  almost  altogether  analyzed  into  matter,  force, 
mind,  and  the  other  categories  which  we  have  been  studying,  it 
follows  that  phenomena  are  often  special  instrumentalisms.  Many 
of  these  apparently  have  been  evolved  in  a  crude  and  haphazard 
manner,  but  almost  all  of  them  possess  some  peculiar  and  highly 
finished  efficiency  property.  As  illustrations  we  may  mention  the 
efficiency  functions  of  wood,  stone,  light,  and  the  change  of  seasons. 

Efficients,  Categories,  and  Phenomena 

As  a  result  of  our  investigations  we  have  therefore  found  three 
general  classes  of  efficiency  instruments,  viz. :  those  which  have  been 
respectively  termed  Efficients,  Categories,  and  Phenomena.  No  one 
of  these  classes  can  be  determined  independently  of  the  other  two, 
and  each  can  be  resolved  largely  into  the  others.  But  in  this  cir- 
cuit of  transformation,  positive  surplusage  everywhere  may  arise, 
and  a  varied  cancellation  of  assumptions  takes  place.  In  this  man- 
ner, from  a  new  and  more  comprehensive  point  of  view,  the  group  is 
made  to  stand  forth  in  the  first  place  both  as  method  and  result,  and 
as  leading  on  to  other  more  ultimate  ideas,  if  such  are  called  for, 
or  are  possible.  We  thus  arrive  at  a  general  conception  of  the 
relation  of  efficiency  to  other  primal  ideas  and  to  a  general  philosophy 
of  life,  which,  in  order  to  obtain  the  advantages  connected  with  a 
name,  we  may  term  efficientism. 


B.     HISTORICAL  SURVEY 

Value  of  History  of  Efficiency  Principles 

A  brief  survey  of  the  historical  development  of  the  principles 
which  have  been  presented  in  this  book  will  be  of  service  in  different 
ways.  For  instance  it  will  clarify  and  develop  these  principles  by 
presenting  them  in  certain  new  relations  to  each  other.  It  will  exhibit 
the  uses  of  the  Efficients  in  the  special  forms  in  which  they  have 
been  applied  in  the  past.  It  may  suggest  new  individual  forms  which 
they  may  take.  It  should  shed  light  on  the  best  places  at  which 
and  methods  by  which  to  apply  these  principles  to  the  present-day 
world.  It  will  also  aid  in  realizing  the  place  of  efficiency  in  a  general 
philosophy  of  life. 

Certain  of  the  primal  efficiency  instruments  (as  uniformities, 
diversities,  groups,  rhythms)  appear,  though  often  in  a  crude  form, 
in  inanimate  nature,  and  in  various  plants  and  animals.  In  man 
also  we  find  them  developed  to  a  certain  point  before  the  dawn  of 
any  distinctive  efficiency  consciousness. 

Primitive  Instruments  of  Efficiency 

We  begin  our  more  detailed  survey  with  a  statement  of  the  initial, 
semi-conscious  efficiency  efforts  of  man.  We  shall  first  present  in 
tabular  form  (see  p.  351)  the  early  instruments  devised  by  man  for 
making  his  exertions  more  productive.  In  this  table  the  conven- 
tional names  for  these  aids  to  efficiency  are  used,  but  we  shall  also 
state  the  more  important  of  them  in  terms  of  the  Efficients. 

Thus  it  will  be  observed  that  each  item  in  the  table,  as  the  use  of 
caves,  clubs,  metals,  and  animals,  involves  externality  of  some  sort. 

Each  of  these  items  also  arises  by  directive  action  of  some  kind, 
and  is  made  more  productive  by  means  of  reuse. 

Each  of  the  tabulated  devices  and  arts  involves  some  species  of 
groupism.  Multiplicative  groupism  appears  in  many  highly  con- 
densed forms,  but  also  in  some  which  are  more  explicit  and  elaborate, 
such  as  tribal  organization  and  articulate  language.  The  order  of 
materials  concept  is  illustrated  in  the  series  of  materials,  wood, 

350 


HISTORICAL  SURVEY 


351 


INORGANIC 

BIOLOGIC 

PSYCHOLOGIC 

SOCIAL 

RELIGIOUS 

Caves  (as  dwel- 

Trees        (as 

Articulate 

Family 

lings) 

dwellings) 

language 

Stones  (as  wea- 

pons) 

Clubs 

Opposable 
thumb 

Right  handed- 
ness 

Wild  animals 
(as  food) 

Pictorial  arts 

Tribalism 

Fetishism 
Taboo 

Shaped  stones 

(as  arrow 

Skins         and 

and       axe 

tendons 

heads,  pes- 

tle        and 

Tomahawk 

Graphic  sym- 

Animism 

mortar) 

(bow  and  ar- 

bols 

row) 

Totemism 

Magic 

Sun-dried  pot- 

tery 

Fire       (baked 

Music 

Exogamy 

pottery) 

Copper 

Domesticated 
Animals 

Written    lan- 
guage 

Confucianism 

Bronze 

Pastoral  life 
(human  sla- 
very) 

Astronomy 
(beginnings 
of  science) 

Iron 

Agriculture 

Steel 

stone,  copper,  bronze,  iron,  steel;  in  right  handedness;  and  in  the 
succession  of  linguistic  forms,  and  of  the  mental  processes  which 
accompanied  these. 


Primitive  Combinations  of  Efficients 

It  should  also  be  realized  that  usually  several  of  the  primal  in- 
struments of  efficiency  are  found  operating  together  in  one  of  the 
items  tabulated  above. 

Thus  man's  erect  position  by  raising  the  eye  to  a  higher  position 
gives  a  larger  outlook  and  hence  increased  externality  in  human  life 
processes.    It  also  leaves  the  hands  free  for  efficiency  functions  which 


352  SOURCES  OF  EFFICIENCY 

are  higher  as  a  whole  than  those  of  the  feet,  and  has  thus  pro- 
duced an  order  of  materials  development  of  man's  limbs,  which  in 
time  has  led  to  the  formation  of  other  orders  of  material. 

The  use  of  fire  constitutes  an  externality  which  is  useful  both 
directly  and  also  indirectly  by  the  formation  of  diversities  and 
re-groupings.  The  resulting  actions  and  reactions  form  a  rhythm  of 
increasing  power. 

Crude  as  it  is  at  first  sight  fetishism  contains  an  important 
externality.  In  fact  in  fetishism  and  like  practices  are  found  the 
germs  of  the  use  of  unlimited  externality,  together  with  certain 
consequent  groupings,  forms  of  reuse,  and  other  efficientizings. 

It  is  important  to  note  that  in  all  this  early  efficiental  life,  sur- 
plusage or  profit  holds  a  dominant  place  as  compared  with  certi- 
tude or  reality.  The  primitive  man  lived  and  worked  for  definite 
and  directly  useful  results.  This  view  of  life  so  far  as  it  is  a  general 
view  or  theory,  takes  the  form  of  what  is  called  animism  or  spiritism 
(or  personeity).  Spiritism  is  essentially  that  view  of  life  in  which 
the  principal  method  of  obtaining  results  is  that  of  treating  all 
nature  processes  as  the  acts  or  under  the  control  of  persons  (beings, 
spirits),  who  can  be  propitiated  and  converted  into  friends  and  help- 
ers. Hence  animism  puts  surplusage  and  the  personal  methods  of 
obtaining  it  in  the  first  place  as  compared  with  the  mechanical 
equivalence  idea  of  life  later  called  natural  law.  The  use  of  spirits 
suggesting  as  it  does  large  immediate  returns  at  little  cost,  appealed 
to  men  in  several  important  ways  and,  for  the  time  being,  was  devel- 
oped in  preference  to  pure  groupism  with  its  better  results  attainable 
after  a  larger  period  of  effort. 

Crude  as  they  were  in  many  respects,  the  essential  efficiencies 
involved  in  man's  first  inventions  and  discoveries  produced  in  the 
aggregate  remarkable  gains.  Thus  land  used  pastorally  was  one 
hundred  times  as  efficient  as  land  used  for  the  hunting  of  wild 
game;  and,  when  used  agriculturally,  was  four  times  as  productive 
as  when  employed  pastorally. 

Efficiencies  in  Early  Empires 

The  large  alluvial  plains  of  Egypt,  Babylonia,  India,  and  China  in 
which  men  first  applied  agriculture  extensively,  fostered  the  devel- 
opment of  efficiency  in  certain  ways,  but  also  gave  rise  to  some 
backward  tendencies.  Such  plains  are  characterized  by  vast  unifor- 
mities which  led  to  the  promotion  of  giant  homogeneous  political. 


HISTORICAL  SURVEY  353 

social,  linguistic,  religious,  and  intellectual  groups.  Often  one  of 
these  vast  groups  in  the  end  took  the  form  of  a  multiplicative 
group  system,  the  most  explicit  example  being  the  empire  of  the 
Medes  and  Persians  with  its  satrapies,  provinces,  and  subprovinces. 
In  each  individual  empire,  and  between  empires,  also  naturally 
developed  forms  and  vast  amounts  of  reuse,  reciprocal  externality, 
directive,  symbolisms,  and  permanencies  in  time.  Hence  also  arose 
important  efficiency  arts  and  sciences,  such  as  systematic  irriga- 
tion in  agriculture,  the  astronomy  of  the  Babylonians,  the  land 
measurement  (or  geometry)  of  the  Egyptians,  and  the  arithmetic 
of  the  Hindoos.  The  large  size  of  the  groups  involved  together  with 
the  accompanying  lack  of  diversity  led  however  to  some  evils,  chief 
among  which  were  certain  extreme  forms  of  uniformity.  Con- 
spicuous illustrations  are  the  caste  system  of  the  Hindoos  and  the 
oriental  doctrine  of  fatalism. 

Similarly  the  category  of  personality  was  developed  in  striking 
ways  in  these  early  civilizations.  One  of  the  more  concrete  forms 
of  such  development  was  Confucianism  among  the  Chinese;  more 
sublimated  species  were  Brahmanism  and  Buddhism  among  the 
Hindoos  and  the  worship  of  Jehovah  among  the  Hebrews.  Be- 
sides giving  other  advantages,  these  highly  developed  views  of 
spiritism  were  useful  in  making  infinite  externaHty  a  near  and 
useful  fact.  Associated  with  these  ideas  were  positive  non-equiva- 
lence, or  surplusage,  taken  as  dominant  over  equivalence  in  the 
form  now  termed  natural  law.  Connected  with  personality  and 
surplusage  in  the  highly  developed  forms  however  were  grave  evils 
such  as  magic  and  necromancy,  certain  views  as  to  miracles,  and 
a  failure  to  recognize  pure  groupism  as  in  many  respects  back 
of  and  dominant  over  personality,  and  leading  to  and  requiring 
important  kinds  of  universal  equivalence  or  law. 

Greeks  discover  the  Group  Principle 

It  is  the  immortal  glory  of  the  Greek  mind  to  have  discovered, 
in  essential  respects,  the  group  as  an  abstract,  primal,  and  inclusive 
principle.  Near  enough  to  Orientalism  to  benefit  by  its  results, 
and  yet  far  enough  away  to  be  able  to  perceive  and  to  attempt 
to  remedy  its  defects,  aided  by  the  geographical  diversity  of  the 
land  in  which  he  lived  and  the  variety  of  its  natural  resources, 
familiar  with  the  sea  and  its  efficiency  uses,  and  influenced  by  other 
factors,  the  Greek  was  led  to  recognize  the  value  of  uniformity 


354  SOURCES  OF  EFFICIENCY 

and  of  grouping.  His  attempts  to  form  comprehensive  efficiency 
systems  along  this  Hne  naturally  at  first  took  somewhat  concrete 
forms. 

As  an  example  we  have  the  views  of  Thales.  In  his  idea  of 
water  as  the  primal  material  out  of  which  all  things  are  made 
•or  generated,  Thales,  in  efifect,  conceived  of  a  universal  first  prin- 
ciple, free  from  the  caprices  of  personality  (but  annexing  the  ele- 
ments of  personality  occasionally  in  a  subordinate  manner),  and 
therefore  capable  of  being  grouped  and  multiplicatively  grouped  in 
reliable  ways,  and  hence  open  to  mechanical  trigger  control. 

Water  of  course  has  radical  imperfections  as  a  first  principle,  and 
other  early  Greek  philosophers  tried  to  get  rid  of  these  by  using 
instead  of  water  some  other  element,  as  air,  fire,  mind,  being,  motion, 
rest,  or  matter.  Of  these  immediate  successors  of  Thales,  Democri- 
tus  performed  the  greatest  service  in  that  he  first  developed  in  explicit 
group  form  some  of  the  properties  latent  in  the  substance  which  he 
regarded  as  primordial,  viz. :  matter.  He  obtained  this  result  by 
regarding  matter  as  divided  into  units  termed  atoms,  and  by  com- 
bining atoms  in  what  were  essentially  groups  to  explain  phenomena. 
The  advantages  thus  attained  are  illustrated  for  instance  in  Democri- 
tus'  theory  of  vision  and  its  consequences  as  presented  elsewhere 

(PP-  335-336). 

All  of  the  early  Greek  thinkers  erred  however  in  paying  primary 
attention  to  the  category  of  reality  and  in  leaving  the  efficiency 
functions  of  their  ideas  to  take  care,  so  to  speak,  of  themselves. 

The  Sophists  performed  a  negative  service  by  showing  that  cer- 
titude and  ultimate  reality  could  not  be  attained  along  the  route 
by  which  these  were  being  pursued.  They  performed  a  more 
positive  service  by  making  gain  or  advantage  the  primary  aim  of  life 
and  by  developing  certain  grammatical  and  rhetorical  groups  and 
multiplicative  group  systems,  of  which  the  moods  and  tenses  of 
verbs  are  examples,  as  instruments  in  attaining  their  ends.  They 
erred  however  in  adopting  narrow  and  superficial  views  as  to  the 
nature  of  gain  and  profit. 

Socrates  was  the  first  to  discover  and  apply  the  group  in  an 
abstract,  general  form.  The  group  as  used  by  him  is  what  is  now 
usually  termed  the  concept.  Socrates  also  developed  this  into  the 
incipient  multiplicative  group  form  embodied  in  the  use  of  the 
terms  genus  and  species.     He  applied  the  group,  as  thus  conceived, 


HISTORICAL  SURVEY  355 

in  the  special  and  somewhat  personal  fields  of  ethics  and  sociology, 
and  not  at  all  in  the  domain  of  natural  science.  His  primary  aim  also 
in  thus  applying  the  group  was  certitude  and  not  utility.  He  could 
not  however  use  it  even  in  this  narrow  way  without  to  a  certain 
extent  developing  its  abstract  and  general  properties.  Hence  the 
work  of  Socrates,  in  spite  of  his  failure  to  give  the  group  a  pure 
subpersonal  form  and  free  development,  constitutes  a  prime  epoch 
in  the  history  of  efficiency. 

Plato  and  Aristotle 

Plato  took  the  group  instrument  invented  by  Socrates  and  de- 
veloped it  in  important  ways.  In  his  hands  it  took  the  form  of 
the  idea  or,  as  we  would  perhaps  describe  it,  the  seen  or  graphic 
efficiental  essence  of  an  object  or  domain,  though  he  often  gave  it 
much  more  general  and  untrammelled  meanings.  For  Plato  sepa- 
rated the  special  form  of  the  group  which  he  termed  the  idea,  from 
the  world  of  concrete  limitation  and  quality,  and  developed  it  freely 
with  respect  to  various  categories.  Thus  owing  to  his  work  the 
group  acquired  a  name,  became  subpersonal,  objective,  self-existent, 
and  creative  of  phenomena.  Plato  not  only  developed  his  group  idea 
in  these  ways,  but  he  also  applied  it  to  all  departments  of  life  and 
knowledge  as  they  then  existed.  In  the  more  abstract  of  these 
departments,  as  in  mathematics,  logic,  ethics,  and  sociology,  he  by 
this  means  obtained  results  of  importance;  but  his  undue  emphasis 
on  certitude  and  his  lack  of  appreciation  of  the  enormous  profusion 
of  highly  developed  diversities  in  the  world,  make  his  investigations 
in  the  field  of  more  concrete  science,  crude  and  unsound.  His  sepa- 
ration, for  the  time  being,  of  ideas  from  the  world  of  concrete 
phenomena,  and  his  consequent  free  and  aggressive  development 
of  their  properties,  form  a  work  of  the  first  importance.  It  is  to 
be  noted  that  in  this  work  of  Plato's  we  find  an  application  of 
diversity,  externality,  and  orders  of  material  in  some  of  their  highest 
forms. 

With  Aristotle  the  group  took  the  specific  and  dominant  form  of 
the  category.  Aristotle  recognized  more  fully  than  did  Plato  the 
fundamental  richness  of  diversity  and  of  individual  quality  in 
phenomena,  and  the  consequent  need  of  using  special  adapted 
primal  forms  of  the  group  when  applying  it  in  different  fields  and 
relations,  and  hence  also  the  need  of  careful  progressive  steps  in 
such  applications.    Among  the  special  forms  in  which  the  group  and 


356  SOURCES  OF  EFFICIENCY 

multiplicative  groups  appear  in  Aristotle,  are  his  categories,  his 
various  kinds  of  causes,  his  syllogisms,  and  his  methods  of  classifi- 
cation and  organization.  In  certain  important  ways  he  also  realizes 
substantiality  or  thinghood  as  subordinate  to  or  as  a  special  cause  of 
grouphood  and  value.  Thus  he  regards  things  as  their  purposes, 
ends,  and  relations,  rather  than  as  the  matter  composing  them. 
Motion  he  also  explains  as  the  result  of  the  desire  of  things  for 
form.  Similarly  matter  according  to  him  is  a  potency  of  form; 
soul  is  an  actuality  of  this;  and  God  is  purus  actus  (or  pure 
groupism) . 

Aristotle's  treatment  of  the  group  lacks  the  freedom  and  sweep 
of  Plato's  but  it  fits  the  details  of  the  naive  phenomenal  world 
far  more  closely.  Because  of  his  careful,  direct  application  of  what 
is  essentially  the  group  method  to  the  facts  of  life  as  they  are 
immediately  apprehended,  Aristotle  was  able  to  initiate  important 
new  departments  of  study  and  efficiency  attainment,  such  as  physics, 
botany,  zoology,  and  medicine,  and  to  put  logic  in  what  is  essentially 
its  present  form. 

Other  similar  products  of  the  Greek  use  of  the  group  were 
sciences  like  psychology,  ethics,  and  esthetics;  or  more  special  pro- 
ducts such  as  Greek  literature,  architecture,  and  sculpture.  To 
this  fundamental  source  also  are  to  be  traced  the  principles  of 
measure,  proportion,  moderation,  and  symmetry,  which  pervaded 
the  Greek  civilization  and  filled  it  with  a  manifold  creative  life. 

Limitations  in  Greek  Grasp  of  Efficiency  Principles 

From  the  ideal  standpoint,  however,  the  Greek  systems  of  effi- 
ciency had  serious  defects.  One  of  these  was  the  failure  to  realize 
the  self -corrective  power  in  the  multiplicative  principle  when  freely 
used.  Hence  results  the  tendency  in  the  Greek  mind  to  invent  and 
employ  elaborate  and  costly  methods  of  preventing  error.  This  char- 
acteristic is  illustrated  by  Aristotle's  use  of  his  system  of  syllo- 
gisms primarily  as  a  means  of  detecting  fallacies,  rather  than  as  a 
method  of  putting  knowledge  in  a  productive  and  readily  usable 
form.  Other  deficiencies  are  the  undue  prominence  given  to  truth 
and  reality  as  aims  and  ends,  and  the  lack  of  a  grasp  and  free  use 
of  infinite  externality. 

Cramped  in  these  ways,  the  Greek  efficiency  systems  were  not 
able  quickly  to  grasp  and  handle  the  world  life  as  a  whole  on  coming 
into  sudden  contact  with  it  after  the  conquests  of  Alexander  the 


HISTORICAL  SURVEY  357 

Great.  Hence  the  primal  Greek  instruments  of  thought  and  action 
came  to  be  used  in  a  narrow  and  personal  way  as  in  Stoicism  and 
Epicureanism,  or  in  a  mystical  and  flighty  way  as  in  Neo-Platonism. 
Hence  while  the  use  of  the  group  concept  continued  to  produce 
certain  useful  results  in  mathematics,  art,  literature,  and  some  de- 
partments of  science,  it  was  prevented  from  quickly  reaping  its 
full  fruitage  by  the  fact  that  its  use  was  made  tributary  to  the 
search  for  a  final  reality. 

Efficiencies  Characteristic  of  Christianity 

The  next  great  advance  in  the  development  of  the  principles  of 
efficiency  was  made  by  Christianity  and  consisted  in  putting  infinite 
externality  in  a  near  and  usable  form.  Orientalism  had  made 
familiar  the  idea  of  the  infinite  group,  but  in  the  unlimited  group  as 
thus  conceived  the  individual  was  lost  and  immersed,  or  with  respect 
to  it  was  regarded  as  insignificant,  the  result  being  a  tendency  to 
fixity  and  fatalism.  On  the  other  hand  in  Christianity  the  individual 
was  conserved,  and  the  infinite  group  had  to  him  the  relation  of 
infinite  e:>fternality  with  all  the  possible  uses  of  the  same.  Thus  in  its 
essence  Christianity  is  a  combination  of  oriental  and  Greek  effi- 
ciency processes.  With  this  union  the  broad  and  complete  founda- 
tion was  laid  for  every  ultimate  advance. 

The  Middle  Ages 

During  the  middle  ages  there  was  steady  progress  in  the  major 
elements  of  efficiency.  Thus  there  was  a  constantly  increasing  appre- 
ciation of  the  brotherhood  of  man  and  the  fatherhood  of  God,  and  of 
the  vast  groupages  which  these  ideas  imply.  The  Greek  system 
^f  groups  was  also  used  to  advantage,  in  a  supplementary  way,  in 
Christian  theology,  and  the  church  was  made  more  effective,  in  some 
respects,  by  the  adoption  of  the  Roman-oriental  system  of  govern- 
mental organization.  However,  in  certain  important  respects  the 
efficiency  life  of  the  world  retrograded  during  the  medieval  epoch. 
The  tendency  to  seek  in  some  easy  and  immediate  way  the  fruits 
latent  in  the  Christian  infinities  was  prominent.  Hence,  following 
the  method  of  Plato,  the  vast  amount  of  concrete  limitation  in  the 
world  and  the  need  for  patient  study  of  detailed  facts,  and  for  their 
grouping  and  regrouping,  were  overlooked,  the  detailed  activities 
of  many  centuries  being  given  up  to  theoretic  speculation,  and 
-mystical  rhapsody.     Nevertheless  the  major  elements  of  efficiency 


358  SOURCES  OF  EFFICIENCY 

which  were  at  work  were  so  powerful  that  important  special  new 
elements  of  efficiency  were  being  discovered  or  invented  from 
time  to  time.  Among  these  advances  were  the  invention  of 
the  horseshoe  which  made  the  age  of  chivalry  possible,  the 
discovery  of  the  magnetic  needle,  the  invention  of  gunpowder, 
the  discovery  of  many  chemical  facts  by  the  alchemists,  and  the 
introduction  into  Europe  of  the  Arabic  arithmetic.  Perhaps  we  may 
fairly  add  to  the  list  the  Copernican  astronomy  with  the  concrete 
externalities,  and  the  re-multiplicative-groupings  which  it  implies, 
and  the  invention  of  printing  by  movable  type  with  the  various  effi- 
ciental  processes  inherent  in  it  and  flowing  from  it. 

Relation  of  Bacon  to  Efficiency  Principles 

Bacon,  like  Aristotle,  realized  the  vast  richness  of  diversity  and 
the  great  variety  of  limitations  which  characterized  the  world  of 
nature  and  life  as  we  find  it.  Hence  he  understood  the  need  of  a 
careful,  methodic  study  of  nature  at  first  hand,  in  order  to  obtain 
results  of  vital  and  permanent  value.  He  advocated  the  patient 
collection  of  facts  and  the  arrangement  of  these  in  groups,  with 
subsequent  constructions  from  them  of  hierarchies  of  inclusive  prin- 
ciples or  laws.  In  other  words,  in  essence  he  urged  the  discovery 
and  formation  of  elementary  groups  and  the  building  up  of  these 
into  multiplicative  group  systems.  Bacon's  use  of  groups  differs 
from  that  of  Aristotle  in  important  particulars.  It  is  superior  in 
its  advocacy  of  the  investigation,  in  cases  of  difficulty,  of  mere 
uniformities  and  diversities ;  in  the  analysis  given  of  the  sources  of 
error  in  the  process  of  forming  groups;  in  a  realization  of  the 
value  of  formal  written  tabulations  of  facts;  in  the  use  of  the  objec- 
tive world  as  the  best  starting  place  for  such  studies;  and  in  the 
orderliness  and  comprehensiveness  of  his  proposed  study  of  the 
objective  world. 

Bacon  however  was  inferior  to  Aristotle  in  that  he  failed  to  realize 
the  value  of  an  early  general  group  schematism,  obtained  from  an 
examination  of  categories  like  space,  time,  substance,  force,  as  well  as 
phenomena,  as  an  aid  in  mastering  facts,  even  though  such  a  schema- 
tism be  subject  to  much  later  modification. 

Of  like  nature  is  Bacon's  failure  to  recognize  the  value  of  the 
working  hypothesis.  Rarely,  if  ever,  has  an  important  discovery 
been  made  by  the  application  of  the  Baconian  method  pure  and 
simple.     The  effective  method  of  arriving  at  multiplicative  group 


HISTORICAL  SURVEY  359 

systems  of  facts,  is  not  to  try  as  a  first  process  to  collect  all  possible 
facts  and  then  at  one  stroke  to  frame  them  into  a  final  system. 
Rather  the  successful  method  is  to  collect  facts  till  an  intelligent 
working  hypothesis,  or  provisional  multiplicative  group  system  can 
be  formed;  to  test  this  provisional  system  by  deduction  (i.e.,  reuse), 
by  experiment  (i.e.,  by  externality  and  the  use  of  units  and  multi- 
pliers) ;  to  arrive  thus  at  new  facts  in  a  far  more  efficient  way  than 
could  otherwise  be  done ;  to  reconstruct  the  working  hypothesis  from 
time  to  time  by  the  aid  of  the  new  facts  thus  obtained;  and  to 
proceed  thus  by  rhythmic  progression  till  a  highly  developed  or  even 
final  result  is  obtained.  An  example  is  the  process  by  which  the  law 
of  gravitation  was  discovered,  extending  as  this  process  does  through 
periods  of  alternate  observation  of  the  heavenly  bodies  and  the 
framing  of  theories  from  the  time  of  the  Babylonians  to  Newton.  A 
more  concise  illustration  is  supplied  by  the  succession  of  steps  by 
which  Darwin  developed  the  doctrine  of  the  evolution  of  species. 

Descartes  and  Leibnitz 

The  general  provisional  multiplicative  group  schematism,  broad 
enough  to  include  the  categories  as  well  as  the  then  known  or  ascer- 
tainable concrete  facts,  which  Bacon  failed  to  make,  was  attempted 
by  Descartes,  Spinoza,  and  others.  The  most  important  of  these 
comprehensive  toolages  for  our  purpose  is  that  of  Leibnitz.  The 
monads  employed  by  him  from  one  point  of  view  are  units  or  ele- 
ments ;  from  another  are  groups ;  and  from  still  another  constitute 
strands  in  a  pluralism.  The  principle  of  preestablished  harmony 
which  in  effect  combines  the  monads,  is  the  group  principle  taken  as 
underlying  and  controlling.  Its  use  in  essence,  makes  subpersonal 
groupism  primal  and  dominant,  and  hence  more  fundamental  than 
either  personality  or  material  mechanism.  The  emphasis  placed  by 
Leibnitz  on  the  principles  of  continuity  and  differentials  also  consti- 
tutes a  recognition  of  the  special  value  of  uniformity  and  diversity. 
Hence  in  the  system  of  Leibnitz  as  a  whole  we  find  our  main  instru- 
ments of  efficiency,  but  in  a  peculiar  and  highly  individualized  form. 
The  value  of  these  principles  even  in  this  form  is  demonstrated  by  the 
important  results  obtained  by  Leibnitz  through  their  use,  the  most 
valuable  of  these  being  the  differential  and  integral  calculus  in 
mathematics. 


360  SOURCES  OF  EFFICIENCY 

Locke  and  His  Successors 

Locke  applied  the  Baconian  method  to  the  domain  of  mind.  His 
aim  was  to  build  up  all  mental  phenomena  out  of  a  few  primal 
elements,  as  all  language  is  formed  out  of  the  alphabet,  or  as  Euclid 
built  up  his  geometry  out  of  a  few  fundamental  properties  of  space. 
Locke  thus  obtained  efficiency  results  of  the  greatest  impvortance. 
These  were  appHed  by  him  and  his  successors,  particularly  in  France, 
not  only  to  psychology,  but  also  to  ethics,  education,  and  government. 

Berkely  and  Hume  ignored  the  economy  and  efficiency  significance 
of  Locke's  work,  and  spent  much  time  and  effort  in  showing  that 
Locke's  method  did  not  reveal  an  ultimate  reality  or  give  fundamental 
certitude.  This  drove  Kant,  like  Socrates  under  similar  circum- 
stances, to  a  recognition  of  the  group.  For  Kant  regards  time, 
space,  and  the  other  categories  as  group  methods  in  which  the  mind 
acts  in  relation  to  the  objective  world,  and  his  synthetic  judgments 
indicate  the  surplusages  or  advantages  which  result.  Notwithstand- 
ing its  great  apparent  emphasis  on  mind  and  personality,  this  point 
of  view  is  closely  related  to  that  which  regards  groupism  as  the 
primal  principle  with  mind,  matter,  space,  time,  etc.,  and  as  special 
modes  in  which  the  group  principle  acts  or  manifests  itself. 

Kant,  Hegel,  and  Herbart 

Kant  also  made  an  important  contribution  to  the  efficiency  schema- 
tism by  obtaining  a  principle  of  certitude  in  his  categorical  impera- 
tive. This  principle  is  arrived  at  in  effect  by  a  use  of  unlimited 
externality  with  a  consequent  order  of  materials  and  dynamic  result. 
Hence  it  constitutes  a  special  manifestation  of  the  self-corrective 
and  unity-giving  power  of  the  multiplicative  principle. 

Hbwever  in  Kant's  system  the  lack  of  explicitness  as  to  whether 
the  group  is  to  be  taken  as  more  fundamental  than  mind  and  matter, 
leaves  the  world  of  principles  and  the  world  of  phenomena  largely 
uncoordinated.  Hegel  tried  to  combine  these  two  worlds  by  taking 
the  ''idea",  which,  in  spite  of  the  element  of  mentality  seemingly 
implied  in  it,  is  fundamentally  a  group  principle,  as  primal  and  con- 
stitutive of  all  things.  By  this  method  he  obtained  many  efficiental 
results,  but  in  its  application  he  failed  to  take  the  principle  of  limi- 
tation and  of  specific  quality  adequately  into  the  account. 

Herbart  avoided  the  element  of  mentality  which  warps  and  cramps 
Hegel's  system  from  the  efficiency  point  of  view,  by  taking  as  a  funda- 
mental principle  what  is  essentially  the  abstract  and   subpersonal 


HISTORICAL  SURVEY  361 

group  discussed  in  Chapter  IV.  This  is  found  in  his  idea  of  particu- 
lars forming  a  unity  (his  realen  and  siisammen).  However  he  retro- 
grades in  that  he  uses  this  fundamental  conception  primarily  as  a 
means  of  obtaining  certitude  or  reality  rather  than  efficiency,  and  in 
that  he  fails  to  realize  its  power  when  developed  as  an  extended  mul- 
tiplicative series  and  in  various  qualitative  forms.  He  nevertheless 
obtained  useful  results  by  an  application  of  his  method  in  the  field 
of  education;  the  most  important  of  these  being  his  principle  of 
apperception.  The  use  of  apperception  in  education  means,  essen- 
tially, the  statement  of  what  is  new  in  the  terms  of  what  is  already 
Icnown.  Hence  in  it  are  contained  the  use  of  uniformity  and  diver- 
sity, reuse,  and  often  of  the  unit  and  multiplier. 

Evolutionary  as  related  to  Efficiency  Principles 

The  method  of  evolution  as  presented  by  Darwin,  Heit)ert 
Spencer,  and  others,  may  be  regarded  as  a  special  combination  of 
certain  efficiency  processes. 

Thus  in  Darwin's  principle  of  the  survival  of  the  fittest  we  have 
a  multiplicative  expansion  of  objects  by  reproduction,  a  resulting 
homogeneous  externality  and  a  re-multiplicative-grouping  into  a 
more  eflfective  system.  The  continuity  characteristic  of  such  a  pro- 
cess involves  an  almost  continuous  stream  of  marginal  reuse,  each 
organism  reusing  almost  in  an  entirety  the  organism  which  preceded 
it  in  the  stream  of  development. 

Similarly  Herbert  Spencer's  more  comprehensive  view  of  evolu- 
tion as  a  series  of  alternate  integrations  and  dissipations  may  be 
viewed  as  a  rhythm  of  groupings,  new  externality,  and  re-groupings. 
In  these  processes  the  principles  of  limitation  and  motion  and  force 
are  also  fully  recognized.  In  certain  forms  of  evolution  still  other 
groups  are  suggested,  as  in  the  idea  of  Mendel  and  de  Vries  that 
the  elements  of  an  organism  may  vary  and  be  adapted  in  groups. 
The  use  of  the  order  of  materials  is  also  suggested  in  the  thought, 
for  instance,  that  the  capacity  of  an  organism  for  variation  may  vary. 

It  is  to  be  observed,  however,  that,  as  ordinarily  considered,  evolu- 
tion is  a  slow  and  costly  system  of  obtaining  results,  as  compared 
with  certain  other  existent  or  conceivable  efficiency  systems.  Thus, 
from  the  ideal  efficiency  standpoint  evolution  is  deficient  because  of 
its  slight  use  of  externality,  orders  of  material,  directive,  symbolisms, 
and  other  similar  highly  efficient  instruments.  Hence,  as  usually 
understood,  it  forms  a  special  detail  in  the  general  efficiency  system 
which  we  are  investigating. 


362  SOURCES  OF  EFFICIENCY 

Concrete  and  Scientific  Developments 

As  has  been  suggested  and  illustrated  at  various  points,  parallel 
with  the  development  of  the  abstract  principles  of  efficiency,  there 
has  proceeded  a  development  of  these  principles  in  certain  more 
concrete  and  special  fields,  as  in  agriculture,  mechanics,  govern- 
ment, and  the  various  arts  and  sciences.  These  two  streams  of 
progress  have  often  interacted  helpfully.  As  an  illustration  of  the 
development  of  the  Efficients  in  one  of  these  special  concrete  forms 
we  may  take  the  changes  which  have  characterized  the  progress  of 
agriculture. 

Similarly  the  progress  of  science,  as  a  whole,  has  been  essentially^ 
a  progressive  development  of  efficiency  instruments  and  methods. 
Thus  the  axioms  and  laws  of  science  are  primarily  fundamental 
instruments  of  efficiency.  For  instance  the  principle  that  action  and 
reaction  are  always  equal  is  a  primary  source  of  economy,  since  when 
either  action  or  reaction  is  known,  the  other  is  known  also,  and  the 
labor  of  an  independent  investigation  of  it  is  saved.  So  also  progress 
in  science  is  made  by  the  extended  use  of  various  kinds  of  auxiliaries^ 
by  units  and  multipliers,  and  reuse,  and  by  combining  results  in  mul- 
tiplicative group  systems  which  are  full  of  both  economy  and  dialectic 
power. 

Pragmatism  and  Its  Services 

The  brief  examination  of  the  history  of  the  principles  of  efficiency 
made  thus  far  shows  that  the  realization  of  these  principles  has 
been  greatly  hindered  by  the  fact  that  throughout  by  far  the  greater 
part  of  definitely  recorded  history,  the  discovery  of  an  ultimate 
reality  has  been  taken  as  the  primary  goal  of  human  endeavor. 
It  would  seem  that  the  concept  of  a  fundamental  reality  cannot  be 
ultimate;  that  if  an  ultimate  were  discovered  we  would  at  once 
proceed  to  put  it  to  certain  uses;  and  that  the  uses  of  this  reality 
would  therefore  be  more  fundamental  than  the  reality  itself.  If 
however  the  human  mind  during  this  long  record  has  been  uncon- 
sciously searching  for  a  fundamental  reality  not  for  its  own  sake,  but 
for  the  sake  of  its  uses,  such  a  fact  has  usually  been  so  far  in  the 
background  that  no  systematic  investigation  of  these  uses,  or  of 
methods  of  their  individual  attainment,  has  been  attempted.  In 
other  words  up  to  within  a  few  years  any  supremacy  attributed  to 
efficiency  or  a  kindred  concept  has  been  unconscious,  or  unsyste- 
matic and  undeveloped. 


HISTORICAL  SURVEY  363 

Recently  however  in  the  movement  termed  pragmatism,  a  con- 
scious and  somewhat  organized  attempt  has  been  made  to  put  utility 
in  the  dominant  place  in  human  thought  and  processes.  According 
to  this  view  of  life  the  certitude  of  a  principle  is  determined  by  the 
consequences  of  that  principle.  Reality  depends  on  workability,  or 
the  useful  is  the  real.  This  view  of  the  matter  seems  to  make  value 
or  surplusage  more  primal  and  determinative  than  reality.  But  by 
their  elaborate  a  priori  discussions  of  the  nature  of  reality  and  by 
requiring  utility  to  satisfy  certain  rationaHstic  tests  laid  down  as 
determinative  of  reality,  the  pragmatic  thinkers  again  in  effect  put 
reality  in  the  first  place.  They  also  do  this  in  a  negative  way  by 
failing  to  make  any  thoroughgoing  examination  and  development  of 
efficiency  methods  and  instruments,  and  by  omitting  to  show  that 
reality  may  be  accounted  for  as  one  of  these  instruments.  The  addi- 
tional failure  to  make  personality  (as  ordinarily  understood)  subor- 
dinate to  efficiency  in  general,  makes  possible  the  chaos  which  arises 
when  each  person  is  allowed  to  construct  his  own  efficiency  (and 
hence  reality)  world,  unharmonized  with  those  of  others  by  any 
systematic  comprehensive  means.  In  other  words  instead  of  making" 
the  group  primary  and  fundamental,  at  least  for  the  time  being,  the 
pragmatic  movement  spends  its  force  in  rationalistic  discussions  of 
the  relations  between  two  special  forms  or  results  of  the  group,  viz. : 
reality  and  personal  utility,  and  alternately  giving  the  dominance  to 
each  of  these.  Even  this  imperfect  treatment  of  the  utility  concept 
however  has  produced  a  number  of  widely  useful  results. 

The  pragmatic  movement,  for  instance,  has,  in  a  measure,  inspired 
the  recent  direct  study  of  efficiency  in  more  or  less  concrete  fields, 
as  in  business  management  and  in  civic  and  governmental  affairs. 
In  these  movements  many  special  results  of  importance  have  been 
arrived  at.  The  more  important  of  these  results  have,  however, 
been  referred  to  in  the  chapters  which  precede,  and  no  repetition 
of  them  is  called  for  at  this  point. 

Summary  of  History  of  Efficiency 

The  preceding  historical  survey  may  be  conveniently  summarized 
as  follows.  In  the  early  stages  of  human  history  we  find  the  group 
utilized  in  the  form  of  the  family,  tribe,  or  clan ;  in  flocks  and  herds ; 
in  various  mechanical  devices;  in  different  kinds  of  language;  and 
in  ideas  as  to  various  forms  of  spirits.    All  this  use  of  the  group 


364  SOURCES  OF  EFFICIENCY 

is  dominated  by  a  naive  assumption  of  gain  or  surplusage  as  primal, 
with  slight  development  of  the  idea  of  reality. 

Later  the  great  alluvial  plains  fostered  the  development  of  enor- 
mously large  groups  both  concrete  and  abstract.    These  larger  groups 
mastered  and  often  absorbed  the  smaller  ones  formed  earlier,  and 
also  those  systems  of  groups  which  came  into  the  great  river  plains 
from  outside  sources,  principally  Aryan.    The  ultimate  result  often 
was  the  formation  of  a  gigantic  multiplicative  group  system,  operated 
from  the  apex,  and  illustrated  by  the  Persian  and  Roman  empires. 
In  contrast  with  this  was  developed  what  may  be  termed  the  federal, 
or  Greek-Christian-Teutonic  multiplicative  group  system.     In  this 
form  of  group  organization  action  originates  mainly  in  the  individual 
tmits  or  elements  and  proceeds  toward  the  apex.    The  system  how- 
ever is  so  full  of  freedom  that  multiplicative  action  also  proceeds 
from  the  apex  toward  the  elements,  and  in  many  cross  and  mixed 
directions.     In  general  the  multiplicative  principle  acting  thus  tends 
to  give  unity  along  with  the  maximum  of  freedom.     The  Greek- 
Christian-Teutonic  method  when  developed  in  the  most  abstract 
and   inclusive  way  gives   rise  to   a   federal   system  of   Efficients, 
acting  in  connection  with  a  similar  but  weaker  system  of  limitations, 
the  two  systems  intersecting  to  form  many  special  agencies  and  re- 
sults.   It  makes  fundamental  neither  the  One  nor  the  Many,  but  the 
One-in-the-Many.    Hence  this  general  schematic  conception  may  be 
regarded  as  including  monism,  dualism,  pluralism,  idealism,  mechan- 
ism, and  the  other  special  systems  touched  upon  in  the  preceding 
historical  survey,  as  details  of  itself,  especially  when  the  systems 
just  mentioned  are  regarded  as  methods  of  obtaining  results. 


INDEX 


Absolute,  347 

Abstract,  105 

Aeroplane,    130,   132 

African,  83 

Agriculture,  2,  10,  16,  22,  41,  96,  138, 

144,  197,  265,  313,  Z()2 
Algebraic  symbols,  173,  183 
Alloys,  133,  134 
Alphabet,  17,  29 
Amoeba,  16,  24,  218 
Anglo-Saxon,  202 
Animism,  351,  352 
Ants,  301 

Apperception,  17,  361 
Arabic  arithmetic,  29,  52,  170,  358 
Architecture,  106 
Aristotle,  251,  355,  358 
Army,  70 
Art,  29,  323 
Assaying,  42 

Astronomy,  17,  19,  96,  141,  212 
Atom,  z^,  96 
Automatic,  31 
Automobile,  15 
Auxiliaries,  28,  124 
Axioms,  339,  362 

Bacon,  260,  275,  358 

Barometer,  165 

Bell,  Graham,  272 

Bessemer,  112 

Biology,  19,  39,  45,  145,  193,  250 

Bird,  136 

Blind,  language  for,  166 

Bogey  efficiency,  6 

Bolometer,  117 

Book,  67,  74,  136 

Bookkeeping,  132 

Botany,  3,  78,  91,  174 

Boy,  157,  294 

Brain,  145 

Bricklaying,  210,  216,  321 

Bridges,  21,  286 

British  Emipire,  51 

Browning,  102 

Burbank,  Luther,  172,  199 

Business,  164,  175,  320 

By-products,  154 


Calculus,  90,  244 
Cancellation,   113 


Carbon  compounds,  3 

Card  index,  j(i,  89,  135 

Caste  system,  103,  147 

Catalysts,  22 

Categories,  ZZZ,  348 

Cause,  223,  344 

Cell,  45 

Change,  222 

Charts,  175,  176 

Chemistry,  3,  89,  144,  160 

Chinese  alphabet,  29,  43,  185 

Christ,  46,  196,  213,  327 

Christianity,  118,  357 

Civilization,  103 

Classification,  86 

Club,  15,  III,  121 

Cold  storage,  114 

Columbus,  249,  311 

Combinations  of  efficients,  301 

Comparative  method,   114 

Competition,  226 

Competitive  efficiency,  7 

Complex  efficiency,  9 

Compromise,  125,  261 

Concrete,  105 

Confucius,  353 

Consciousness,  123,  346 

Conservation,  194 

Conservation  of  energy,  140 

Constitutive  multiplicative  groups,  74 

Continuity,  143 

Corporation,  18 

Crane,  traveling,  19 

Crookes,  William,  249 

Dante,  324,  325 

Darwin,    Charles,    17,    146,    275,    293, 

345,  361 
Darwin,  G,  H,,  237 
Death  rate,  2 
Democritus,  335,  354 
Descartes,  359 
Dialectic,  249 
Dictionary,  80 
Diesel  engine,  i,  2 
Diet,  102 

Digestion,  119,  136 
Directive,  192 
Diversity,  130 
Division  of  labor,  138 
Domestic  work,  314 


36s 


366 


INDEX 


Domesticated  animals,  i6 
Drum  signals,  165 
Duality,  125,  142 
Dynamic,  210,  223 
Dynamo,  65 

Economy,  7,  23,  61,  79,  80,  90,  loi,  117, 

174,  etc. 
Eddies,  back,  223,  239 
Education,  99,  125,  131,  313 
Efficacy,  8 
Efficiency,  i,  4,  etc. 
Efficiency  engineer,  197,  210 
Efficientism,  349 
Efficients,  67 
Efficiental,  67 
Efficiental  essence,  173 
Egypt,  353 

Electricity,  42,  63,   138,  303 
Electrification,  62 
Elements  of  a  group,  64 
Emerson,  Harrington,  i 
Energy,  17,  62 
English  government,  304 
English  weights  and  measures,  276 
Enzymes,  22 
Equivalence,  8,  143,  154 
Erect  position,  253,  351 
Error,  281 
Esperanto,  186 
Ether,  96,  115,  336 
Ethics,  285,  ■^2'] 
Euclid,  338 
Euler,  178 

Evolution,  45,  260,  361 
Exercise,  p'hysical,  106 
Expenditures  and  results,  152 
Externality,  11 1 

Family,  60 
Family  tree,  ^2,  78 
Faraday,  272,  293,  336 
Federal  group  system,  73 
Fetichism,  351,  352 
Food,  102 

Foremen,  functional,  26 
Formulas,  78,  221 
France.  192 
Franklin,  62 
Freights,  102 
Fuegians,  17 

Galvanometer,  39 
Gang  plow,  57,  139 
Gas  engine,  39 
Generalization,  43,  140 
Genius,  311,  317 


Geography,  29 

Geology,   125,   168,  233,  237 

Geometry,  339 

Geometric  symbols,  173,  184 

German  agriculture,  278 

Glass  making,  118 

Gold,  42 

Golf,  212 

Government,  82,  84,  85,  319,  320 

Gravitation,  121,  130,  145 

Great  men,  120,  311,  317 

Greek,  25,  276,  320,  353,  356 

Group,  56 

Gun  firing,  265 

Habit,  303 

Harvey,  345 

Hegel,  360 

Hellriegel,  254 

Henry,  Joseph,  136 

Herbart,  360 

Herz,  237 

Heterogeneous  efficiency,  5,  160 

Hindoos,  353 

History,  201,  287,  350 

Homogeneous  efficiency,  5,  160 

Hook  eyelet,  53 

Horse  power,  36,  yj 

Human  body,  efficiency  of,  303 

Humus,  3 

Hypothesis,  working,  89,  359 

Imitation,  22 

Induction,  mathematical,  24 

Inertia,  220,  272 

Infinite  efficiency,  8 

Infinity,  341 

Influence,  22 

Initiative,  201,  204 

Insects,  301 

Insurance,  life,  102 

Invar,  134 

Inverse  groups,  59 

Ion,  96,  147 

Irrigation,  115,  196 

Jackson,  Stonewall,  239 

James,  William,  63 

Japan,  23 

Jehovah,  171,  185,  353 

Joule,  62 

Joy,  120 

Jurisprudence,  98,  104 

Kant,  118,  259,  287,  360 
Keller,  Helen,  183 
Kelvin,  340 


INDEX 


367 


Kepler,  160 
Kinematic,  210,  222 
Koch,  146 
Krupp',  275 

Labor,  unskilled,  i 

Language,  19,  74,  186,  351 

Latitude,  and  longitude,  74,  78 

Leibnitz,  359 

Lens,  38,  254,  269,  274 

Lever,  24,  ^8 

Library,  travelling,  21 

Life,  345 

Lignite,  8,  201 

Limitation,  265 

Linear  multiplicative  groups,  76,  88 

Linneus,  90,  185 

Locke,  360 

Logic,  21,  112,  356 

Lucifer  match,  22 

Machinery,  79,  82,  121 

Maize,  137 

Man,  definitions  of,   120 

Marginal  multiplicative  groups,  74 

Marginal  reuse,  19 

Mathematics,  82,  183 

Matter,  96,  103,  243,  335 

Mayer,  62 

Mechanism,  343 

Medievalism,  357 

Mendel,  361 

Mendeleveff,  237 

Metal  cutting,  9,  218 

Metaphysics,  106 

Microphone,  45 

Microscope,    115 

Mill,  J.  S.,  336 

Mind,  346 

Money,  97,  99,   107,   130,   181 

Mosquito,  29 

Motion,  210,  344 

Mottled  efficiency,  305 

Moving  pictures,  24 

Multiplicative  groups,  70 

Multipliers,  34 

Multuse,  34,  175 

Napoleon,  119,  195,  224,  274,  284,  289. 

294,  312 
Navigation,  121 
Negative  reuse,  21 
Neighborhood  isymbolism,  90,  167 
New  England,  89,  252 
Newspapers,  158 
Newton,  Isaac,  25,  130,  160 
Niagara  Falls,  51 


Non-equivalence,  156 
Number,  339 

Oersted,  62 

Oolites,  39 

Opportunistic  efficiency,  302 

Order,  21 

Orders  of  groups,  71 

Orders  of  material,  95 

Organization,  86 

Outflank,  116 

Panama  Canal,  i 
Paradox,  281,  291 
Parallel  efficiency,  9 
Pascal,  286 
Pasteur,  258 
Patience,  125 
Paul,  46 
Peaty  soils,  288 
Pedagogy,  114,  313 
Perkin,  W.  H.,  249,  258 
Persia,  353 
Personality,  346 
Phenomena,  349 
Photography,  42,   138,    145 
Physics,    126 
Pigeon  holes,  79 
Plant  breeding,  51 
Plato,  63,  251,  340,  355,  357 
Polar  dialectic,  252 
Positive  non-equivalence,  27,  156 
Post  Office,  123 
Potential,  223 
Pragmatism,  362 
Preventive  medicine,  20 
Priestly,  Joseph,  176 
Prophetic  reuse,  20 
Psychological  moment,  40 
Psychology,    16,   39,   83,   96,   166,  277, 
309,  346 

Qualitative  efficiency,  6 
Quality,  342 
Quantity,  340 

Race  suicide  319 
Radium,  65 
Railroad,  62,  80,  225 
Ramsay,  William,  238 
Reality,  154,  337,  355,  363 
Reaper,  96 

Reciprocating  action,  232 
Rectangular  network,  79 
Religion,  46,  122,  285,  329 
Relativity,  65,  87,   106,   124,    182,   183, 
205,  etc. 


368 


INDEX 


Relative  efficiency,  4,  6 
Resultant  efficiency,  9 
Reuse,  15 
Rhetoric,  102 
Rhythm,  230 
Roentgen  (see  X  rays) 
Roman  Catholic  Church,  'jz,  74 
Rotation  of  crops,  240,  302 
Rothschilds,  113,  217 
Rural  free  delivery,  249 

Salesmen,  18 

Savage,  15,  11 1 

Schools,  58,  62 

School  houses,  21 

Science,  2^,  52,  89,  160,  317,  362 

Scientific  management,  210,  320 

Seasons,  change  of,  22,(i 

Semi-linear  multiplicative  groups,  76 

Serum,  42 

Sewage,  242 

Sewing  machine,  132 

Shakespeare  25,  28,  102 

Shorthand,  185 

Shrewdness,  304 

Slight-of-hand,  285 

Slide  rule,  91,  225 

Sociology,  40,  97,  i59,  3 18 

Socrates,  282,  354 

Sophists,  354 

Space,  85,  123,  170,  204,  333,  338 

Spectroscope,  19 

Speed,  210,  217 

Spencer,  Herbert,  30,  361 

Spider,  iii 

Spiritism,  352 

Stafif  organization,  78 

Starch,  137 

Steamboat,  20 

Steam  engine,  i,  6,  9,  39,  130,  243 

Steel,  283 

Strandal  multilplicative  groups,  75 

Strategic  point,  40 

Subject,  346 

Subpersonal,  156 

Substance,  337 

Suez  Canal,  i 

Suffrage,  universal,  37 

Sugar  beets,  6,  267 

Summary,  general,  301,  306 

Summum  bonum,  278 

Surgery,  130 

Surplusage,  27,  156 

Surveyor,  164 

Syllogism,  282,  356 

Symbolism,  164 

Symmetry,  135 


Symphony,  178 
Syndicate,  press,  34 
System,  86 

Taboo,  351 

Tandem  efficiency,  9 

Tape  worm,  30 

Taylor,  F.  W.,  26,  225,  230,  2"]-],  32Q 

Teleology,  152,  344 

Telegraphy,  34,  39,  136,  171,  I99 

Telephone,  39,  74,  80,  117 

Telescope,  115 

Temperate  zone,  136 

Thales,  354 

Thoreau,  117 

Tides,  230,  236 

Time,  343 

Titanic,  loss  of,  219,  271,  291 

Transformations      of      multiplicative 

groups,  89 
Transportation,  98,  121 
Trigonometry,  26 
Tubular  boiler,  136 
Tropism,  193 
Truth,  133,  153,  160 
Tugboat,  20,  135 
Tungsten,  5 
Twenty  Questions,  game  of,  "72 

Uniformity,  130 

Unit,  34 

United  States,  46,  62,  196,  252,  270 

Universal  machine,  20 

Universal  suffrage,  yj 

Usefulness,  8 

Utility,  8 

Utilization,  204 

Value,    155 
Van  t'Hoff,  139 
Von  Moltke,  196 

Wallace,  Alfred,  146,  275 
Warning  colors,  165 
Watt,  James,  130,  201 
Wave  motion,  232 
Weather  bureau,  116 
Westinghouse,  George,  21,  257 
Wireless  telegraphy,  178 
Worth,  155 

X  rays,   119,   186,  252 

Yellow  fever,  119 

Zebra,  141 

Zero,  112,  164,  341 


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